Fire Incident Dispatch Data Analysis
Zuliani Riccardo
12/12/2023
1 Loads & Install Packages
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## combinelibrary(nnet)
library(MASS)
library(e1071)
library(class)
library(leaps)
library(glmnet)
library(car)
library(caTools)
library(mgcv)
library(summarytools)
library(dplyr)
library(ggplot2)
library(tidyverse)
library(lubridate)
library(mapview)
library(sf)
library(geojsonio)
library(leaflet)
library(broom)
library(plotly)
library(gridExtra)2 Dataset description
The Fire Incident Dispatch Data file contains data that is generated by the Starfire Computer Aided Dispatch System. The data spans from the time the incident is created in the system to the time the incident is closed in the system. It covers information about the incident as it relates to the assignment of resources and the Fire Department’s response to the emergency. To protect personal identifying information in accordance with the Health Insurance Portability and Accountability Act (HIPAA), specific locations of incidents are not included and have been aggregated to a higher level of detail.
In this analysis we have restricted the analysis only on the last 50.000 observations from 5th of September to 30th of the same month.
STARFIRE_INCIDENT_ID: An incident identifier comprising the 5 character julian date, 4 character alarm box number, 2 character number of incidents at the box so far for the day, 1 character borough code , 4 character sequence number.
INCIDENT_DATETIME: The date and time of the incident.
ALARM_BOX_BOROUGH: The borough of the alarm box.
ALARM_BOX_LOCATION: The location of the alarm box.
ALARM_BOX: The alarm box number.
INCIDENT_BOROUGH: The borough of the incident.
ZIPCODE: The zip code of the incident.
POLICEPRECINCT: The police precinct of the incident.
CITYCOUNCILDISTRICT: The city council district.
COMMUNITYDISTRICT: The community district.
COMMUNITYSCHOOLDISTRICT: The community school district.
CONGRESSIONALDISTRICT: The congressional district.
ALARM_SOURCE_DESCRIPTION_TX: The description of the alarm source.
ALARM_LEVEL_INDEX_DESCRIPTION: The alarm level index.
HIGHEST_ALARM_LEVEL: The highest alarm level.
INCIDENT_CLASSIFICATION: The incident classification.
INCIDENT_CLASSIFICATION_GROUP: The incident classification roll up group.
FIRST_ASSIGNMENT_DATETIME: The date and time of the first unit assignment.
FIRST_ACTIVATION_DATETIME: The date and time of the first unit acknowledgement of the assignment.
FIRST_ON_SCENE_DATETIME: The date and time of the first unit at the scene of the incident.
INCIDENT_CLOSE_DATETIME: The date and time that the incident was closed in the dispatch system.
VALID_DISPATCH_RSPNS_TIME_INDC: Indicates that the components comprising the generation of the DISPATCH_RESPONSE_SECONDS_QY are valid.
DISPATCH_RESPONSE_SECONDS_QY: The elapsed time in seconds between the incident_datetime and the first_assignment_datetime.
VALID_INCIDENT_RSPNS_TIME_INDC: Indicates that the components comprising the generation of the INCIDENT_RESPONSE_SECONDS_QY are valid.
INCIDENT_RESPONSE_SECONDS_QY: The elapsed time in seconds between the incident_datetime and the first_onscene_datetime.
INCIDENT_TRAVEL_TM_SECONDS_QY: The elapsed time in seconds between the first_assignment_datetime and the first_onscene_datetime.
ENGINES_ASSIGNED_QUANTITY: The number of engine units assigned to the incident.
LADDERS_ASSIGNED_QUANTITY: The number of ladder units assigned to the incident.
OTHER_UNITS_ASSIGNED_QUANTITY: The number of units that are not engines or ladders that were assigned to the incident.
Regarding the response we will try create two different analysis. One with the aim to predict the INCIDENT_RESPONSE_SECONDS_QY and the other to predict the EMERGENCY_TIME which is the time difference between the FIRST_ON_SCENE_DATETIME and INCIDENT_CLOSE_DATETIME. Both analysis use a linear regression model, however we will see that the assumption for applying the linear regression will be not meet, thus we will simplify our project moving into classification, dividing in two or more ranges the two responses.
3 Data Exlporation and Cleaning
The first step is always to read the dataset and plot the first 5 observations
fire_data <- read.csv("datasets/Fire_Incident_Dispatch_Data_last_50k.csv")
head(fire_data)## STARFIRE_INCIDENT_ID INCIDENT_DATETIME ALARM_BOX_BOROUGH
## 1 230905-B1937-001-0567 09/05/2023 02:19:04 PM BROOKLYN
## 2 230905-B3923-002-0568 09/05/2023 02:19:36 PM BROOKLYN
## 3 230905-X8897-003-0480 09/05/2023 02:19:43 PM BRONX
## 4 230905-X3466-001-0481 09/05/2023 02:21:00 PM BRONX
## 5 230905-B2448-001-0570 09/05/2023 02:21:26 PM BROOKLYN
## 6 230905-B2448-002-0571 09/05/2023 02:22:35 PM BROOKLYN
## ALARM_BOX_NUMBER ALARM_BOX_LOCATION INCIDENT_BOROUGH
## 1 1937 AUTUMN AVE & FULTON ST BROOKLYN
## 2 3923 N/S EASTERN PWAY & UTICA AVE BROOKLYN
## 3 8897 CROSS BX EXPY- DEEGAN EX TO JEROME AV BRONX
## 4 3466 ADEE AVE & BX PARK E BRONX
## 5 2448 GLENWOOD RD & BEDFORD AVE BROOKLYN
## 6 2448 GLENWOOD RD & BEDFORD AVE BROOKLYN
## ZIPCODE POLICEPRECINCT CITYCOUNCILDISTRICT COMMUNITYDISTRICT
## 1 11208 75 37 305
## 2 11213 71 35 309
## 3 NA NA NA NA
## 4 10467 49 12 211
## 5 11210 70 45 314
## 6 11210 70 45 314
## COMMUNITYSCHOOLDISTRICT CONGRESSIONALDISTRICT ALARM_SOURCE_DESCRIPTION_TX
## 1 19 7 EMS
## 2 17 9 CLASS-3
## 3 NA NA EMS-911
## 4 11 15 EMS
## 5 22 9 EMS
## 6 22 9 EMS
## ALARM_LEVEL_INDEX_DESCRIPTION HIGHEST_ALARM_LEVEL
## 1 Initial Alarm First Alarm
## 2 Initial Alarm First Alarm
## 3 Initial Alarm First Alarm
## 4 DEFAULT RECORD First Alarm
## 5 DEFAULT RECORD First Alarm
## 6 DEFAULT RECORD First Alarm
## INCIDENT_CLASSIFICATION INCIDENT_CLASSIFICATION_GROUP
## 1 Medical - No PT Contact EMS is Onscene Medical Emergencies
## 2 Hospital Fire Structural Fires
## 3 Vehicle Accident - Other NonMedical Emergencies
## 4 Medical - EMS Link 10-91 Medical Emergencies
## 5 Medical - EMS Link 10-91 Medical Emergencies
## 6 Medical - EMS Link 10-91 Medical Emergencies
## DISPATCH_RESPONSE_SECONDS_QY FIRST_ASSIGNMENT_DATETIME
## 1 7 09/05/2023 02:19:12 PM
## 2 95 09/05/2023 02:21:11 PM
## 3 41 09/05/2023 02:20:25 PM
## 4 298 09/05/2023 02:25:59 PM
## 5 25 09/05/2023 02:21:52 PM
## 6 350 09/05/2023 02:28:25 PM
## FIRST_ACTIVATION_DATETIME FIRST_ON_SCENE_DATETIME INCIDENT_CLOSE_DATETIME
## 1 09/05/2023 02:19:26 PM 09/05/2023 02:25:23 PM 09/05/2023 03:03:15 PM
## 2 09/05/2023 02:21:33 PM 09/05/2023 02:23:21 PM 09/05/2023 02:34:18 PM
## 3 09/05/2023 02:20:35 PM 09/05/2023 02:26:22 PM 09/05/2023 04:13:32 PM
## 4 09/05/2023 02:26:04 PM 09/05/2023 02:34:23 PM
## 5 09/05/2023 02:22:08 PM 09/05/2023 02:28:07 PM
## 6 09/05/2023 02:29:09 PM
## VALID_DISPATCH_RSPNS_TIME_INDC VALID_INCIDENT_RSPNS_TIME_INDC
## 1 N Y
## 2 N Y
## 3 N Y
## 4 N N
## 5 N N
## 6 N N
## INCIDENT_RESPONSE_SECONDS_QY INCIDENT_TRAVEL_TM_SECONDS_QY
## 1 378 371
## 2 224 129
## 3 398 357
## 4 NA NA
## 5 NA NA
## 6 NA NA
## ENGINES_ASSIGNED_QUANTITY LADDERS_ASSIGNED_QUANTITY
## 1 1 0
## 2 3 2
## 3 2 3
## 4 1 0
## 5 1 0
## 6 1 0
## OTHER_UNITS_ASSIGNED_QUANTITY
## 1 0
## 2 1
## 3 1
## 4 0
## 5 0
## 6 0Use dfSummary from summarytool in order to have a complete and clear sumamry of the dataset.
print(dfSummary(fire_data,
plain.ascii = FALSE,
style = "multiline",
headings = FALSE,
graph.magnif = 0.8,
valid.col = FALSE),
method = 'render')| No | Variable | Stats / Values | Freqs (% of Valid) | Graph | Missing | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | STARFIRE_INCIDENT_ID [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 2 | INCIDENT_DATETIME [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 3 | ALARM_BOX_BOROUGH [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 4 | ALARM_BOX_NUMBER [integer] |
|
7411 distinct values |  |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 5 | ALARM_BOX_LOCATION [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 6 | INCIDENT_BOROUGH [character] |
|
|
|
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 7 | ZIPCODE [integer] |
|
217 distinct values |  |
3181 (6.4%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 8 | POLICEPRECINCT [integer] |
|
77 distinct values |  |
3180 (6.4%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 9 | CITYCOUNCILDISTRICT [integer] |
|
51 distinct values |  |
3180 (6.4%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 10 | COMMUNITYDISTRICT [integer] |
|
70 distinct values |  |
3180 (6.4%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 11 | COMMUNITYSCHOOLDISTRICT [integer] |
|
32 distinct values |  |
3182 (6.4%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 12 | CONGRESSIONALDISTRICT [integer] |
|
13 distinct values |  |
3180 (6.4%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 13 | ALARM_SOURCE_DESCRIPTION_TX [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 14 | ALARM_LEVEL_INDEX_DESCRIPTION [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 15 | HIGHEST_ALARM_LEVEL [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 16 | INCIDENT_CLASSIFICATION [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 17 | INCIDENT_CLASSIFICATION_GROUP [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 18 | DISPATCH_RESPONSE_SECONDS_QY [integer] |
|
841 distinct values |  |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 19 | FIRST_ASSIGNMENT_DATETIME [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 20 | FIRST_ACTIVATION_DATETIME [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 21 | FIRST_ON_SCENE_DATETIME [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 22 | INCIDENT_CLOSE_DATETIME [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 23 | VALID_DISPATCH_RSPNS_TIME_INDC [character] | 1. N |
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 24 | VALID_INCIDENT_RSPNS_TIME_INDC [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 25 | INCIDENT_RESPONSE_SECONDS_QY [integer] |
|
1496 distinct values |  |
14112 (28.2%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 26 | INCIDENT_TRAVEL_TM_SECONDS_QY [integer] |
|
1382 distinct values |  |
14112 (28.2%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 27 | ENGINES_ASSIGNED_QUANTITY [integer] |
|
15 distinct values |  |
62 (0.1%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 28 | LADDERS_ASSIGNED_QUANTITY [integer] |
|
12 distinct values |  |
62 (0.1%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 29 | OTHER_UNITS_ASSIGNED_QUANTITY [integer] |
|
23 distinct values |  |
62 (0.1%) |
Generated by summarytools 1.0.1 (R version 4.3.2)
2024-01-14
Now we rename all the columns in order to be smaller whenever we plot graphs.
fire_data <- fire_data %>%
rename(id = STARFIRE_INCIDENT_ID, datetime = INCIDENT_DATETIME, al_borough = ALARM_BOX_BOROUGH,
al_number = ALARM_BOX_NUMBER,al_location = ALARM_BOX_LOCATION, inc_borough = INCIDENT_BOROUGH,
zipcode = ZIPCODE, pol_prec = POLICEPRECINCT, city_con_dist = CITYCOUNCILDISTRICT,
commu_dist = COMMUNITYDISTRICT, commu_sc_dist = COMMUNITYSCHOOLDISTRICT,
cong_dist = CONGRESSIONALDISTRICT, al_source_desc = ALARM_SOURCE_DESCRIPTION_TX,
al_index_desc = ALARM_LEVEL_INDEX_DESCRIPTION, highest_al_level = HIGHEST_ALARM_LEVEL,
inc_class = INCIDENT_CLASSIFICATION, inc_class_group = INCIDENT_CLASSIFICATION_GROUP,
first_ass_datetime = FIRST_ASSIGNMENT_DATETIME, first_act_datetime = FIRST_ACTIVATION_DATETIME,
first_onscene_datetime = FIRST_ON_SCENE_DATETIME, inc_close_datetime = INCIDENT_CLOSE_DATETIME,
disp_resp_sec_qy = DISPATCH_RESPONSE_SECONDS_QY, disp_resp_sec_indc = VALID_DISPATCH_RSPNS_TIME_INDC,
inc_resp_sec_qy = INCIDENT_RESPONSE_SECONDS_QY, inc_resp_sec_indc = VALID_INCIDENT_RSPNS_TIME_INDC,
inc_travel_sec_qy = INCIDENT_TRAVEL_TM_SECONDS_QY,
engines_assigned = ENGINES_ASSIGNED_QUANTITY,
ladders_assigned = LADDERS_ASSIGNED_QUANTITY, others_units_assigned = OTHER_UNITS_ASSIGNED_QUANTITY)As we can see from the summary there are many NA values, and many predictors that are as characters and not factors. In this step we will convert the characters predictors as factors merging the values that appear less in the dataset, so we do no have many values that have low frequency in our dataset.
In addition we will add he predictor for the day_number, a factorial predictor to indicate in the incident day is a week day or not dat_type and a factorial predictor time_of_day that indicates the range of time whenever the incident happens, so Night (if the hour is between 0 and 6), Morning (if the hour is between 6 and 12), Afternoon (if the hour is between 12 and 18), Evening (if the hour is between 18 and 24).
Since we are dealing with datetime we also check if the differences (inc_resp_sec_qy, inc_travel_sec_qy and disp_resp_sec_qy) are actually corrects, if not we replace them with the correct one.
Finally we decided to add an additional time difference the emergency_min_qy which represents the difference between the inc_close_datetime and the first_onscene_datetime.
# set factorial
fire_data$inc_borough <- as.factor(fire_data$inc_borough)
fire_data$al_borough <- as.factor(fire_data$al_borough)
fire_data$al_source_desc <- as.factor(fire_data$al_source_desc)
fire_data$al_index_desc <- as.factor(fire_data$al_index_desc)
fire_data$highest_al_level <- as.factor(fire_data$highest_al_level)
fire_data$disp_resp_sec_indc <- as.factor(fire_data$disp_resp_sec_indc)
levels(fire_data$disp_resp_sec_indc)<- c("N", "Y")
fire_data$inc_resp_sec_indc <- as.factor(fire_data$inc_resp_sec_indc)
levels(fire_data$inc_resp_sec_indc)<- c("N", "Y")
fire_data$inc_class_group <- as.factor(fire_data$inc_class_group)
fire_data$inc_class <- as.factor(fire_data$inc_class)Moreover we note that the maximum level of the time differences is very high to be considered as seconds so we decided to scale the two indicators in minutes.
summary(fire_data %>% select(inc_resp_sec_qy, inc_travel_sec_qy, disp_resp_sec_qy))## inc_resp_sec_qy inc_travel_sec_qy disp_resp_sec_qy
## Min. : 18.0 Min. : 0.0 Min. : 2.00
## 1st Qu.: 265.0 1st Qu.: 233.0 1st Qu.: 7.00
## Median : 334.0 Median : 301.0 Median : 19.00
## Mean : 380.7 Mean : 340.5 Mean : 39.96
## 3rd Qu.: 426.0 3rd Qu.: 392.0 3rd Qu.: 40.00
## Max. :7130.0 Max. :7122.0 Max. :9023.00
## NA's :14112 NA's :14112# scaling
fire_data$inc_resp_sec_qy <- fire_data$inc_resp_sec_qy / 60
fire_data$inc_travel_sec_qy <- fire_data$inc_travel_sec_qy / 60
fire_data$disp_resp_sec_qy <- fire_data$disp_resp_sec_qy / 60
# renaming both quantity and indicator predictors for the two datetime
fire_data <- fire_data %>% rename(inc_resp_min_qy = inc_resp_sec_qy, inc_travel_min_qy = inc_travel_sec_qy, disp_resp_min_qy = disp_resp_sec_qy, # quantity
inc_resp_min_indc = inc_resp_sec_indc, disp_resp_min_indc = disp_resp_sec_indc) # indicatorHere we create the time_of_day and is_weekend
# Process datetime column
fire_data$datetime <- mdy_hms(fire_data$datetime)
fire_data$first_ass_datetime <- mdy_hms(fire_data$first_ass_datetime)
fire_data$first_act_datetime <- mdy_hms(fire_data$first_act_datetime)
fire_data$first_onscene_datetime <- mdy_hms(fire_data$first_onscene_datetime)
fire_data$inc_close_datetime <- mdy_hms(fire_data$inc_close_datetime)
# checking if the differences are well computed if not change with the correct one
if (!identical(fire_data$inc_resp_min_qy, as.numeric(difftime(fire_data$first_onscene_datetime, fire_data$datetime, units="mins")))){
fire_data$inc_resp_min_qy <- as.numeric(difftime(fire_data$first_onscene_datetime, fire_data$datetime, units="mins"))
}
if (!identical(fire_data$inc_travel_min_qy, as.numeric(difftime(fire_data$first_onscene_datetime, fire_data$first_ass_datetime, units="mins")))){
fire_data$inc_travel_min_qy <- as.numeric(difftime(fire_data$first_onscene_datetime, fire_data$first_ass_datetime, units="mins"))
}
if (!identical(fire_data$disp_resp_min_qy, as.numeric(difftime(fire_data$first_ass_datetime, fire_data$datetime, units="mins")))){
fire_data$disp_resp_min_qy <- as.numeric(difftime(fire_data$first_ass_datetime, fire_data$datetime, units="mins"))
}
# creating emergency_min_qy which describe the time taken by the firefighter to close the emergency after have been arrived to the location
fire_data$emergency_min_qy <- as.numeric(difftime(fire_data$inc_close_datetime, fire_data$first_onscene_datetime, units="mins"))
# creating day_type
fire_data$day_type <- as.factor(ifelse(weekdays(fire_data$datetime) %in% c("sabato", "domenica"), "Weekend", "Weekday"))
# creating ticket_time
fire_data$ticket_time <- as.numeric(difftime(fire_data$inc_close_datetime, fire_data$datetime, units="mins"))
# creating time_of_day
fire_data$time_of_day <- cut(
hour(fire_data$datetime),
breaks = c(0, 6, 12, 18, 24),
labels = c("Night", "Morning", "Afternoon", "Evening"),
include.lowest = TRUE,
right = TRUE
)
fire_data$datetime <- NULLtable(fire_data$time_of_day)##
## Night Morning Afternoon Evening
## 8521 13270 16499 11710ggplot(data=fire_data %>%
group_by(time_of_day) %>%
summarise(incident_number = n()),
aes(x=time_of_day, y=incident_number)) +
geom_bar(stat="identity", position=position_dodge()) +
geom_text(aes(label=incident_number), vjust=1.6, color="white", position = position_dodge(0.9), size=3.5) +
labs(title = "Time of the Day - Incident Count", x = "Time of the Day", y = "Incident Count")
From this we can see that the higher number of fire incident is registered from 12 PM to 18 PM, whereas the lower number of fire incident happened from the 00 AM to 06 AM.
day_type_table <- table(fire_data$day_type)
day_type_table[1] <- day_type_table[1] / 5
day_type_table[2] <- day_type_table[2] / 2
day_type_table##
## Weekday Weekend
## 7296.4 6759.0And in proportion we can see that on average there is an higher number of fire incident on the week day respect to the week end days.
Now regarding the assigned untis we decided to add a summary predictor that include the sum of all the three assigned units predictors.
fire_data$total_assigned_unit <- fire_data$engines_assigned + fire_data$ladders_assigned + fire_data$others_units_assignedRename the factor levels for the inc_borough and predictors
fire_data <- fire_data %>% mutate(inc_borough = recode_factor(
inc_borough, "BRONX" = "Bronx", "BROOKLYN" = "Brooklyn", "MANHATTAN" = "Manhattan",
"QUEENS" = "Queens", "RICHMOND / STATEN ISLAND" = "Staten Island"),
al_borough = recode_factor(
al_borough, "BRONX" = "Bronx", "BROOKLYN" = "Brooklyn", "MANHATTAN" = "Manhattan",
"QUEENS" = "Queens", "RICHMOND / STATEN ISLAND" = "Staten Island"))At this point we merge some possible value from factorial predictors to make the space of possible choice smaller.
Here we merge the following factorial values of highest_al_level: Second Alarm and Third Alarm into 2nd-3rd Alarm.
# highest_al_level
fire_data$highest_alarm_lev_new <- fire_data$highest_al_level
levels(fire_data$highest_alarm_lev_new) <- list(
"All Hands Working" = "All Hands Working",
"First Alarm" = "First Alarm",
"2nd-3rd Alarm" = c("Second Alarm", "Third Alarm")
)
print(ctable(fire_data$highest_al_level, fire_data$highest_alarm_lev_new, prop = 'n', totals = FALSE, headings = FALSE), method = 'render')| highest_alarm_lev_new | |||
|---|---|---|---|
| highest_al_level | All Hands Working |
First Alarm | 2nd-3rd Alarm |
| All Hands Working | 100 | 0 | 0 |
| First Alarm | 0 | 49891 | 0 |
| Second Alarm | 0 | 0 | 8 |
| Third Alarm | 0 | 0 | 1 |
Generated by summarytools 1.0.1 (R version 4.3.2)
2024-01-14
fire_data$highest_al_level <- fire_data$highest_alarm_lev_new
fire_data$highest_alarm_lev_new <- NULLHere we merge the following factorial values of al_index_desc: Second Alarm, Third Alarm, 7-5 (All Hands Alarm), 10-76 & 10-77 Signal (Notification Hi-Rise Fire) and 10-75 Signal (Request for all hands alarm) into Others.
# al_index_desc
fire_data$alarm_level_idx_new <- fire_data$al_index_desc
levels(fire_data$alarm_level_idx_new) <- list(
"DEFAULT RECORD" = "DEFAULT RECORD",
"Initial Alarm" = "Initial Alarm",
"Others" = c("Second Alarm", "Third Alarm", "7-5 (All Hands Alarm)",
"10-76 & 10-77 Signal (Notification Hi-Rise Fire)",
"10-75 Signal (Request for all hands alarm)")
)
print(ctable(fire_data$al_index_desc, fire_data$alarm_level_idx_new, prop = 'n', totals = FALSE, headings = FALSE), method = 'render')| alarm_level_idx_new | |||
|---|---|---|---|
| al_index_desc | DEFAULT RECORD |
Initial Alarm |
Others |
| 10-75 Signal (Request for all hands alarm) | 0 | 0 | 13 |
| 10-76 & 10-77 Signal (Notification Hi-Rise Fire) | 0 | 0 | 3 |
| 7-5 (All Hands Alarm) | 0 | 0 | 100 |
| DEFAULT RECORD | 17313 | 0 | 0 |
| Initial Alarm | 0 | 32562 | 0 |
| Second Alarm | 0 | 0 | 8 |
| Third Alarm | 0 | 0 | 1 |
Generated by summarytools 1.0.1 (R version 4.3.2)
2024-01-14
fire_data$al_index_desc <- fire_data$alarm_level_idx_new
fire_data$alarm_level_idx_new <- NULLHere we merge the following factorial values of al_source_desc: 911, 911TEXT, VERBAL, BARS, ERS, ERS-NC and SOL into Others.
fire_data$alarm_source_desc_new <- fire_data$al_source_desc
levels(fire_data$alarm_source_desc_new) <- list(
"PHONE" = "PHONE",
"EMS" = "EMS",
"EMS-911" = "EMS-911",
"CLASS-3" = "CLASS-3",
"Others" = c("911", "911TEXT", "VERBAL", "BARS", "ERS", "ERS-NC", "SOL")
)
print(ctable(fire_data$al_source_desc, fire_data$alarm_source_desc_new, prop = 'n', totals = FALSE, headings = FALSE), method = 'render')| alarm_source_desc_new | |||||
|---|---|---|---|---|---|
| al_source_desc | PHONE | EMS | EMS-911 | CLASS-3 | Others |
| 911 | 0 | 0 | 0 | 0 | 302 |
| 911TEXT | 0 | 0 | 0 | 0 | 14 |
| BARS | 0 | 0 | 0 | 0 | 1 |
| CLASS-3 | 0 | 0 | 0 | 5025 | 0 |
| EMS | 0 | 17178 | 0 | 0 | 0 |
| EMS-911 | 0 | 0 | 10520 | 0 | 0 |
| ERS | 0 | 0 | 0 | 0 | 777 |
| ERS-NC | 0 | 0 | 0 | 0 | 1 |
| PHONE | 15146 | 0 | 0 | 0 | 0 |
| SOL | 0 | 0 | 0 | 0 | 5 |
| VERBAL | 0 | 0 | 0 | 0 | 1031 |
Generated by summarytools 1.0.1 (R version 4.3.2)
2024-01-14
fire_data$al_source_desc <- fire_data$alarm_source_desc_new
fire_data$alarm_source_desc_new <- NULLView again the dataset summary to see the applied changes.
print(dfSummary(fire_data,
plain.ascii = FALSE,
style = "multiline",
headings = FALSE,
graph.magnif = 0.8,
valid.col = FALSE),
method = 'render')| No | Variable | Stats / Values | Freqs (% of Valid) | Graph | Missing | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | id [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 2 | al_borough [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 3 | al_number [integer] |
|
7411 distinct values |  |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 4 | al_location [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 5 | inc_borough [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 6 | zipcode [integer] |
|
217 distinct values |  |
3181 (6.4%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 7 | pol_prec [integer] |
|
77 distinct values |  |
3180 (6.4%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 8 | city_con_dist [integer] |
|
51 distinct values |  |
3180 (6.4%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 9 | commu_dist [integer] |
|
70 distinct values |  |
3180 (6.4%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 10 | commu_sc_dist [integer] |
|
32 distinct values |  |
3182 (6.4%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 11 | cong_dist [integer] |
|
13 distinct values |  |
3180 (6.4%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 12 | al_source_desc [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 13 | al_index_desc [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 14 | highest_al_level [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 15 | inc_class [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 16 | inc_class_group [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 17 | disp_resp_min_qy [numeric] |
|
850 distinct values |  |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 18 | first_ass_datetime [POSIXct, POSIXt] |
|
49509 distinct values |  |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 19 | first_act_datetime [POSIXct, POSIXt] |
|
49205 distinct values |  |
139 (0.3%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 20 | first_onscene_datetime [POSIXct, POSIXt] |
|
35552 distinct values |  |
14112 (28.2%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 21 | inc_close_datetime [POSIXct, POSIXt] |
|
49409 distinct values |  |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 22 | disp_resp_min_indc [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 23 | inc_resp_min_indc [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 24 | inc_resp_min_qy [numeric] |
|
1497 distinct values |  |
14112 (28.2%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 25 | inc_travel_min_qy [numeric] |
|
1369 distinct values |  |
14112 (28.2%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 26 | engines_assigned [integer] |
|
15 distinct values |  |
62 (0.1%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 27 | ladders_assigned [integer] |
|
12 distinct values |  |
62 (0.1%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 28 | others_units_assigned [integer] |
|
23 distinct values |  |
62 (0.1%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 29 | emergency_min_qy [numeric] |
|
4429 distinct values |  |
14112 (28.2%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 30 | day_type [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 31 | ticket_time [numeric] |
|
4870 distinct values | |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 32 | time_of_day [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 33 | total_assigned_unit [integer] |
|
35 distinct values |  |
62 (0.1%) |
Generated by summarytools 1.0.1 (R version 4.3.2)
2024-01-14
3.1 Dealing with invalid values
The next step is to deal invalid values and delete some un-useful predictors.
First of all we saw the possibility that al_borough and inc_borough represent the same column, let’s chek it.
identical(fire_data$al_borough, fire_data$inc_borough)## [1] TRUEThe column `al_borough and inc_borough have the same sequence of values, so we can delete one of the two.
fire_data <- fire_data %>% select(-c(al_borough))Then we say that all observation in the dataset have the disp_resp_min_indc equal to N, let’s check again and in affermative case then we can delete both columns.
summary(fire_data$disp_resp_min_indc)## N Y
## 50000 0All our observations have non valid disp_resp_min_indc so we could delete both the column indicator and the respective column quantity disp_resp_min_qy. However we note that also in the original dataset all the observation have the disp_resp_min_indc set to N, which is quite strange, and seems that is problem relative to the data acquisition, thus we decide to mantein this time difference.
fire_data <- fire_data %>% select(-c(disp_resp_min_indc))Now we do a quick check also on the other indicator variable inc_resp_min_indc
summary(fire_data$inc_resp_min_indc)## N Y
## 17036 32964But here we have some observations with valid inc_resp_min_indc, and we will consider only the valid one deleting the one that has a non valid attribute.
However before doing that let’s see the distribution of inc_resp_min_qy around the borough.
ggplot(data=fire_data %>% group_by(inc_borough, inc_resp_min_indc) %>% summarise(incident_number = n()),
aes(x=inc_borough, y=incident_number, fill=inc_resp_min_indc)) +
geom_bar(stat="identity", position=position_dodge()) +
geom_text(aes(label=incident_number), vjust=1.6, color="white",
position = position_dodge(0.9), size=3.5) +
scale_fill_brewer(palette="Paired") +
labs(title = "Incident Count - Borouh - Valid Response Time in Minutes", x = "Borough", y = "Incident Number", fill = "Valid Response\n Time in Minutes")## `summarise()` has grouped output by 'inc_borough'. You can override using the
## `.groups` argument.
We can see that the number of fire incident is higher for the valid response time in minutes but, it is much interesting observe the rateo between the valid and the non valid.
And to the rateo of valid inc_resp_min_indc in each borough is:
rateo_inc_resp_min_indc <- fire_data %>%
group_by(inc_borough, inc_resp_min_indc) %>%
summarise(incident_number = n()) %>%
mutate(ratio=incident_number/sum(incident_number))## `summarise()` has grouped output by 'inc_borough'. You can override using the
## `.groups` argument.ggplot(rateo_inc_resp_min_indc, aes(fill=inc_resp_min_indc, y=ratio, x=inc_borough)) +
geom_bar(position="fill", stat="identity") +
geom_text(aes(label=scales::percent(ratio)), position=position_fill(vjust=0.5)) +
labs(title="Borough - Rateo Incident between Valid and Invalid",
x="Borough",
y="Rateo Incident between Valid and Invalid",
fill="Valid Response\nTime in Minutes")
And we can see that Staten Island has the higher number of incidents with valid inc_resp_min_indc , whereas Manhattan has the lower number, but remember that the former has the lowest number of fire incident and the latter has the higher number of incident.
Now we do an additional analysis to see if there is some find of relation between the inc_resp_min_indc and total_assigned_unit.
ggplot(fire_data, aes(total_assigned_unit, inc_resp_min_qy)) +
geom_point(aes(colour = inc_resp_min_indc))+
labs(title = "Total Assigned Units - Response Time In Minutes", x = "Total Assigned Units", y = "Response Time In Minutes", colour = "Valid Response\n Time in Minutes")## Warning: Removed 14116 rows containing missing values (`geom_point()`).
We note that the majority of fire incident that had been assigned a single units has a high response time and the relative measure is not valid. Whereas for an higher number of total units the response time decrease and becomes valids.
ggplot(fire_data %>% filter(inc_resp_min_indc == "N")
, aes(total_assigned_unit, inc_resp_min_qy)) +
geom_point(aes(colour = inc_class_group, shape = inc_class_group)) +
labs(title = "Total Assigned Units - Response Time In Minutes - Incidnet Class Group", x = "Total Assigned Units", y = "Response Time In Minutes", colour = "Incident Class Groups")## Warning: Removed 14112 rows containing missing values (`geom_point()`).
Regarding the incident class group around all the incidents with invalid response time had been assigned a single units as we discussed before, but in addition we found that are from the Medical Emergencies, whereas almost all the other incidents are from the NonMedical Emergencies.
# add an additional predictor
fire_data$tua_is_one <- as.factor(ifelse(fire_data$total_assigned_unit == 1, "Y", "N"))
tua_is_one <- fire_data %>%
filter(inc_resp_min_indc == "N", inc_class_group == "Medical Emergencies") %>%
group_by(inc_borough, tua_is_one) %>%
summarise(incident_number = n())## `summarise()` has grouped output by 'inc_borough'. You can override using the
## `.groups` argument.ggplot(data=tua_is_one,
aes(x=inc_borough, y=incident_number, fill=tua_is_one)) +
geom_bar(stat="identity", position=position_dodge()) +
geom_text(aes(label=incident_number), vjust=1.5, color="black",
position = position_dodge(0.9), size=3.5) +
scale_fill_brewer(palette="Set1") +
labs(title = "Total Assigned Units One or Not", x = "Borough", y = "Incident Count", fill = "Total Assigned\nUnits are One")
We have also added an additional factorial predictor tua_is_one to indicates if the total assigned units is equal to one or not.
Continuing we decide to analyse the type of Incident Class of the invalid incidents response time that had been assigned a single total units.
ggplot(data=fire_data %>%
filter(inc_resp_min_indc == "N", inc_class_group == "Medical Emergencies", tua_is_one == "Y") %>%
group_by(inc_class, inc_borough) %>%
summarise(incident_number = n()),
aes(x=inc_borough, y=incident_number, fill=inc_class)) +
geom_bar(stat="identity", position=position_dodge()) +
geom_text(aes(label=incident_number), vjust=1.6, color="black",
position = position_dodge(0.9), size=3) +
scale_fill_brewer(palette="Set1") +
labs(title = "Borough - Incident Counts - Incident Class -- for Total Assigned Units equal to 1", x = "Borough", y = "Incident Counts", fill = "Incident Class Group")## `summarise()` has grouped output by 'inc_class'. You can override using the
## `.groups` argument.
And we found that the majority of the incident that respect these circumstances are mostly identified as Medical - EMS Link 10-91 and Medical - PD Link 10-91.
Thanks to the 10code site we found a description of the two emergency codes:
10-91 Medical Emergency EMS - Fire Unit Not Required - To be transmitted through borough dispatcher by the responding unit when the fire Unit is canceled enroute due to EMS on scene, or EMS downgrades the job to a segment that does not require a Fire Unit response. Note: This signal shall be used only for medical emergency incidents. EMS we are sure that stands for Emergency Medical Services.
10-91 Medical Emergency PD - Fire Unit Not Required - To be transmitted through borough dispatcher by the responding unit when the fire Unit is canceled enroute due to PD on scene, or PD downgrades the job to a segment that does not require a Fire Unit response. Note: This signal shall be used only for medical emergency incidents. PD we think that stands for Police Department.
Now we can look for the NonMedical Emergencies by first see the distribution of its incident class.
print(fire_data %>%
filter(inc_resp_min_indc == "N", inc_class_group == "NonMedical Emergencies") %>%
group_by(inc_class) %>%
summarise(incident_number = n()))## # A tibble: 24 Ă— 2
## inc_class incident_number
## <fct> <int>
## 1 Alarm System - Defective 10
## 2 Alarm System - Testing 22
## 3 Alarm System - Unnecessary 110
## 4 Assist Civilian - Non-Medical 828
## 5 Carbon Monoxide - Code 1 - Investigation 25
## 6 Carbon Monoxide - Code 2 - Incident (1-9 ppm) 4
## 7 Carbon Monoxide - Code 3 - Emergency (over 9 ppm) 4
## 8 Defective Oil Burner 5
## 9 Downed Tree 28
## 10 Elevator Emergency - Occupied 104
## # â„ą 14 more rowsggplot(data=fire_data %>%
filter(inc_resp_min_indc == "N", inc_class_group == "NonMedical Emergencies", inc_class == "Assist Civilian - Non-Medical") %>%
group_by(inc_borough) %>%
summarise(incident_number = n()),
aes(x=inc_borough, y=incident_number)) +
geom_bar(stat="identity", position=position_dodge()) +
geom_text(aes(label=incident_number), vjust=1.6, color="white", position = position_dodge(0.9), size=3.5) +
labs(title = "Incident Count - Borouh - Valid Response Time in Second", x = "Borough", y = "Incident Count")
And we found that the majority of non valid inc_resp_min_indc that are Non-Medical Emergency are from the incident class equal to Assist Civilian - Non-Medical.
For stake of consistency we will consider only the valid observations that have inc_resp_min_indc == "Y".
fire_data <- fire_data %>% filter(inc_resp_min_indc == "Y")
dim(fire_data)## [1] 32964 32Now we want to know how many inc_class are summarized in each inc_class_group, to be sure that each inc_class_group is referred to a single inc_class.
print(ctable(fire_data$inc_class, fire_data$inc_class_group, totals = FALSE, headings = FALSE), method = 'render')| inc_class_group | ||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| inc_class | Medical Emergencies |
Medical MFAs | NonMedical Emergencies |
NonMedical MFAs |
NonStructura l Fires |
Structural Fires |
||||||||||||||||||
| Abandoned Derelict Vehicle Fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 6 | ( | 100.0% | ) | 0 | ( | 0.0% | ) |
| Alarm System - Defective | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 377 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Alarm System - Testing | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 706 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Alarm System - Unnecessary | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 2735 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Assist Civilian - Non-Medical | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 3312 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Automobile Fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 101 | ( | 100.0% | ) | 0 | ( | 0.0% | ) |
| Brush Fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 24 | ( | 100.0% | ) | 0 | ( | 0.0% | ) |
| Carbon Monoxide - Code 1 - Investigation | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 788 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Carbon Monoxide - Code 2 - Incident (1-9 ppm) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 129 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Carbon Monoxide - Code 3 - Emergency (over 9 ppm) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 88 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Carbon Monoxide - Code 4 - No Detector Activation | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 8 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Church Fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 10 | ( | 100.0% | ) |
| Defective Oil Burner | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 34 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Demolition Debris or Rubbish Fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 272 | ( | 100.0% | ) | 0 | ( | 0.0% | ) |
| Downed Tree | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 280 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Elevator Emergency - Occupied | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 1850 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Elevator Emergency - Unoccupied | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 708 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Factory Fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 1 | ( | 100.0% | ) |
| Hospital Fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 18 | ( | 100.0% | ) |
| Manhole Fire - Blown Cover | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 9 | ( | 100.0% | ) | 0 | ( | 0.0% | ) |
| Manhole Fire - Other | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 55 | ( | 100.0% | ) | 0 | ( | 0.0% | ) |
| Manhole Fire - Seeping Smoke | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 104 | ( | 100.0% | ) | 0 | ( | 0.0% | ) |
| Maritime Emergency | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Maritime Fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Medical - Assist Civilian | 27 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Medical - Breathing / Ill or Sick | 4779 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Medical - EMS Link 10-91 | 1096 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Medical - No PT Contact EMS is Onscene | 4285 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Medical - PD Link 10-91 | 868 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Medical - Serious Life Threatening | 366 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Medical - Victim Deceased | 287 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Medical MFA - EMS Link | 0 | ( | 0.0% | ) | 87 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Medical MFA - PD Link | 0 | ( | 0.0% | ) | 77 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Multiple Dwelling 'A' - Compactor fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 4 | ( | 100.0% | ) |
| Multiple Dwelling 'A' - Food on the stove fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 519 | ( | 100.0% | ) |
| Multiple Dwelling 'A' - Other fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 168 | ( | 100.0% | ) |
| Multiple Dwelling 'B' Fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 85 | ( | 100.0% | ) |
| Non-Medical 10-91 (Unnecessary Alarm) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 102 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Non-Medical MFA - ERS | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 586 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Non-Medical MFA - ERS No Contact | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 1 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Non-Medical MFA - Phone | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 701 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Non-Medical MFA - Private Fire Alarm | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 223 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Non-Medical MFA - Verbal | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 7 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Odor - Other Smoke | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 166 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Odor - Other Than Smoke | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 1317 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Other Commercial Building Fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 184 | ( | 100.0% | ) |
| Other Public Building Fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 4 | ( | 100.0% | ) |
| Other Transportation Fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 14 | ( | 100.0% | ) | 0 | ( | 0.0% | ) |
| Private Dwelling Fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 412 | ( | 100.0% | ) |
| Remove Civilian - Non-Fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 27 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| School Fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 31 | ( | 100.0% | ) |
| Sprinkler System - Activated | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 6 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Sprinkler System - Malfunction | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 41 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Sprinkler System - Working on System | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 28 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Store Fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 9 | ( | 100.0% | ) |
| Transit System - NonStructural | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 59 | ( | 100.0% | ) | 0 | ( | 0.0% | ) |
| Transit System - Structural | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 1 | ( | 100.0% | ) |
| Transit System Emergency | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 18 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Undefined Emergency | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 71 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Under Contruction / Vacant Fire | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 1 | ( | 100.0% | ) |
| Utility Emergency - Electric | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 595 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Utility Emergency - Gas | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 1335 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Utility Emergency - Steam | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 137 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Utility Emergency - Undefined | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 4 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Utility Emergency - Water | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 1157 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Vehicle Accident - Other | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 1443 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
| Vehicle Accident - With Extrication | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 21 | ( | 100.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) | 0 | ( | 0.0% | ) |
Generated by summarytools 1.0.1 (R version 4.3.2)
2024-01-14
As we can see from the upper table all the inc_class_group have a unique set of values.
At this point to be more clear we display each main class with each respective sub-class.
for (variable in levels(fire_data$inc_class_group)) {
non_zero_table <- table(subset(fire_data, inc_class_group == variable)$inc_class)
cat(variable, "\n")
print(non_zero_table[non_zero_table != 0])
cat("\n")
}## Medical Emergencies
##
## Medical - Assist Civilian Medical - Breathing / Ill or Sick
## 27 4779
## Medical - EMS Link 10-91 Medical - No PT Contact EMS is Onscene
## 1096 4285
## Medical - PD Link 10-91 Medical - Serious Life Threatening
## 868 366
## Medical - Victim Deceased
## 287
##
## Medical MFAs
##
## Medical MFA - EMS Link Medical MFA - PD Link
## 87 77
##
## NonMedical Emergencies
##
## Alarm System - Defective
## 377
## Alarm System - Testing
## 706
## Alarm System - Unnecessary
## 2735
## Assist Civilian - Non-Medical
## 3312
## Carbon Monoxide - Code 1 - Investigation
## 788
## Carbon Monoxide - Code 2 - Incident (1-9 ppm)
## 129
## Carbon Monoxide - Code 3 - Emergency (over 9 ppm)
## 88
## Carbon Monoxide - Code 4 - No Detector Activation
## 8
## Defective Oil Burner
## 34
## Downed Tree
## 280
## Elevator Emergency - Occupied
## 1850
## Elevator Emergency - Unoccupied
## 708
## Non-Medical 10-91 (Unnecessary Alarm)
## 102
## Odor - Other Smoke
## 166
## Odor - Other Than Smoke
## 1317
## Remove Civilian - Non-Fire
## 27
## Sprinkler System - Activated
## 6
## Sprinkler System - Malfunction
## 41
## Sprinkler System - Working on System
## 28
## Transit System Emergency
## 18
## Undefined Emergency
## 71
## Utility Emergency - Electric
## 595
## Utility Emergency - Gas
## 1335
## Utility Emergency - Steam
## 137
## Utility Emergency - Undefined
## 4
## Utility Emergency - Water
## 1157
## Vehicle Accident - Other
## 1443
## Vehicle Accident - With Extrication
## 21
##
## NonMedical MFAs
##
## Non-Medical MFA - ERS Non-Medical MFA - ERS No Contact
## 586 1
## Non-Medical MFA - Phone Non-Medical MFA - Private Fire Alarm
## 701 223
## Non-Medical MFA - Verbal
## 7
##
## NonStructural Fires
##
## Abandoned Derelict Vehicle Fire Automobile Fire
## 6 101
## Brush Fire Demolition Debris or Rubbish Fire
## 24 272
## Manhole Fire - Blown Cover Manhole Fire - Other
## 9 55
## Manhole Fire - Seeping Smoke Other Transportation Fire
## 104 14
## Transit System - NonStructural
## 59
##
## Structural Fires
##
## Church Fire
## 10
## Factory Fire
## 1
## Hospital Fire
## 18
## Multiple Dwelling 'A' - Compactor fire
## 4
## Multiple Dwelling 'A' - Food on the stove fire
## 519
## Multiple Dwelling 'A' - Other fire
## 168
## Multiple Dwelling 'B' Fire
## 85
## Other Commercial Building Fire
## 184
## Other Public Building Fire
## 4
## Private Dwelling Fire
## 412
## School Fire
## 31
## Store Fire
## 9
## Transit System - Structural
## 1
## Under Contruction / Vacant Fire
## 13.2 NA Patterns?
At this point is essential to deal with NA values, trying to find the presence of possible relation with predictors. First things first let’s recap the number of NA values for each columns that we have at the moment.
colSums(is.na(fire_data))## id al_number al_location
## 0 0 0
## inc_borough zipcode pol_prec
## 0 2197 2197
## city_con_dist commu_dist commu_sc_dist
## 2197 2197 2198
## cong_dist al_source_desc al_index_desc
## 2197 0 0
## highest_al_level inc_class inc_class_group
## 0 0 0
## disp_resp_min_qy first_ass_datetime first_act_datetime
## 0 0 41
## first_onscene_datetime inc_close_datetime inc_resp_min_indc
## 0 0 0
## inc_resp_min_qy inc_travel_min_qy engines_assigned
## 0 0 4
## ladders_assigned others_units_assigned emergency_min_qy
## 4 4 0
## day_type ticket_time time_of_day
## 0 0 0
## total_assigned_unit tua_is_one
## 4 43.2.1 Checking the location predictors
Here we will check if there is a pattern on the absence of values in the following predictors: zipcode, pol_prec, city_con_dist, commu_dist, commu_sc_dist and cong_dist.
na_locations <- fire_data %>%
filter(is.na(zipcode) | is.na(pol_prec) | is.na(city_con_dist) | is.na(commu_dist) | is.na(commu_sc_dist) | is.na(cong_dist))ggplot(data=na_locations %>%
group_by(inc_class_group, inc_borough) %>%
summarise(incident_number = n()),
aes(x=inc_borough, y=incident_number, fill=inc_class_group)) + geom_bar(stat="identity", position=position_dodge()) +
geom_text(aes(label=incident_number), vjust=1.6, color="black",
position = position_dodge(0.9), size=3.5) +
#scale_fill_brewer(palette="Paired") +
labs(title = "NA location", x = "Borough", y = "Incident Count", fill = "Incident Class Group")## `summarise()` has grouped output by 'inc_class_group'. You can override using
## the `.groups` argument.
By the Bar Chart we note that the majority of observations that have at least one of the location predictors to NA are of the incident class group NonMedical Emergency, Non Medical MFAs and Medical Emergencies
table(na_locations$inc_borough) / table(fire_data$inc_borough)##
## Bronx Brooklyn Manhattan Queens Staten Island
## 0.07104538 0.04694547 0.07662157 0.07700328 0.07523697table(na_locations$inc_class_group) / table(fire_data$inc_class_group)##
## Medical Emergencies Medical MFAs NonMedical Emergencies
## 0.03988726 0.10975610 0.05691243
## NonMedical MFAs NonStructural Fires Structural Fires
## 0.40447958 0.14906832 0.00552868Moreover around the 40% of the whole incident that are of the incident class group NonMedical MFAs have at least one of the location columns to NA. Let’s investigate.
fd_nm_mfa_cl <- table(subset(fire_data, inc_class_group == "NonMedical MFAs")$inc_class)
fd_nm_mfa_bro <- table(subset(fire_data, inc_class_group == "NonMedical MFAs")$inc_borough)
fd_nm_mfa_cl <- fd_nm_mfa_cl[fd_nm_mfa_cl != 0]
fd_nm_mfa_cl##
## Non-Medical MFA - ERS Non-Medical MFA - ERS No Contact
## 586 1
## Non-Medical MFA - Phone Non-Medical MFA - Private Fire Alarm
## 701 223
## Non-Medical MFA - Verbal
## 7In the original dataset this is the distribution of inc_class for the NonMedical MF
na_nm_mfa_cl <- table(subset(na_locations, inc_class_group == "NonMedical MFAs")$inc_class)
na_nm_mfa_bro <- table(subset(na_locations, inc_class_group == "NonMedical MFAs")$inc_borough)
na_nm_mfa_cl <- na_nm_mfa_cl[names(fd_nm_mfa_cl)]
na_nm_mfa_cl##
## Non-Medical MFA - ERS Non-Medical MFA - ERS No Contact
## 573 1
## Non-Medical MFA - Phone Non-Medical MFA - Private Fire Alarm
## 38 2
## Non-Medical MFA - Verbal
## 0na_nm_mfa_cl / fd_nm_mfa_cl##
## Non-Medical MFA - ERS Non-Medical MFA - ERS No Contact
## 0.97781570 1.00000000
## Non-Medical MFA - Phone Non-Medical MFA - Private Fire Alarm
## 0.05420827 0.00896861
## Non-Medical MFA - Verbal
## 0.00000000So the 97% of all the Non-Medical MFA - ERS observations in the entire dataset have one of the location attribute equal to NA
na_nm_mfa_bro / fd_nm_mfa_bro##
## Bronx Brooklyn Manhattan Queens Staten Island
## 0.4676056 0.3075221 0.3894472 0.3733333 0.7954545And from here we can see that about the 78% of the observations that are NonMedical - MFAs that have at least one district column attribute to NA are from the RICHMOND / STATEN ISLAND. Also BRONX has about half of the NonMedical - MFAs observations that have at least one district column to NA.
3.2.2 Checking the assigned units predictors
print(fire_data %>%
filter(is.na(engines_assigned) | is.na(ladders_assigned) | is.na(others_units_assigned)) %>%
group_by(inc_borough, inc_class)) %>%
summarise(incident_count = n())## # A tibble: 4 Ă— 32
## # Groups: inc_borough, inc_class [4]
## id al_number al_location inc_borough zipcode pol_prec city_con_dist
## <chr> <int> <chr> <fct> <int> <int> <int>
## 1 230905-Q4545… 4545 53 AVE & 6… Queens 11378 104 30
## 2 230914-Q1014… 1014 CENTRAL AV… Queens 11691 101 31
## 3 230918-Q9643… 9643 JAMAICA AV… Queens 11418 102 29
## 4 230919-M0684… 684 1 AVE & E … Manhattan 10016 13 4
## # â„ą 25 more variables: commu_dist <int>, commu_sc_dist <int>, cong_dist <int>,
## # al_source_desc <fct>, al_index_desc <fct>, highest_al_level <fct>,
## # inc_class <fct>, inc_class_group <fct>, disp_resp_min_qy <dbl>,
## # first_ass_datetime <dttm>, first_act_datetime <dttm>,
## # first_onscene_datetime <dttm>, inc_close_datetime <dttm>,
## # inc_resp_min_indc <fct>, inc_resp_min_qy <dbl>, inc_travel_min_qy <dbl>,
## # engines_assigned <int>, ladders_assigned <int>, …## `summarise()` has grouped output by 'inc_borough'. You can override using the
## `.groups` argument.## # A tibble: 4 Ă— 3
## # Groups: inc_borough [2]
## inc_borough inc_class incident_count
## <fct> <fct> <int>
## 1 Manhattan Vehicle Accident - Other 1
## 2 Queens Assist Civilian - Non-Medical 1
## 3 Queens Medical - No PT Contact EMS is Onscene 1
## 4 Queens Medical - PD Link 10-91 1We can easily remove this observations.
3.2.3 Checking the first_act_datetime predictors
na_first_act_datetime <- fire_data %>% filter(is.na(first_act_datetime))print(na_first_act_datetime %>% group_by(inc_class, inc_borough) %>% summarise(incident_count = n()))## `summarise()` has grouped output by 'inc_class'. You can override using the
## `.groups` argument.## # A tibble: 27 Ă— 3
## # Groups: inc_class [15]
## inc_class inc_borough incident_count
## <fct> <fct> <int>
## 1 Alarm System - Unnecessary Brooklyn 2
## 2 Assist Civilian - Non-Medical Bronx 1
## 3 Assist Civilian - Non-Medical Brooklyn 4
## 4 Assist Civilian - Non-Medical Queens 1
## 5 Demolition Debris or Rubbish Fire Brooklyn 1
## 6 Downed Tree Manhattan 1
## 7 Downed Tree Queens 1
## 8 Downed Tree Staten Island 1
## 9 Elevator Emergency - Occupied Brooklyn 1
## 10 Elevator Emergency - Occupied Manhattan 1
## # â„ą 17 more rowsggplot(data=na_first_act_datetime %>%
group_by(inc_class_group, inc_borough) %>%
summarise(incident_number = n()),
aes(x=inc_borough, y=incident_number, fill=inc_class_group)) + geom_bar(stat="identity", position=position_dodge()) +
labs(title = "NA First Act Date", x = "Borough", y = "Incident Count", fill = "Incident Class Group")## `summarise()` has grouped output by 'inc_class_group'. You can override using
## the `.groups` argument.
Seems to be random and thus there is no pattern that motivate the presence of NA values in first_act_datetime.
At this point we can omit the NA values.
fire_data_new <- na.omit(fire_data)And the un-usefull predictors
fire_data_new <- fire_data_new %>% select(-c(zipcode, pol_prec, city_con_dist, commu_dist, al_location,
commu_sc_dist, cong_dist, first_ass_datetime, first_act_datetime,
first_onscene_datetime, inc_close_datetime, inc_resp_min_indc,
id, al_number, inc_class))print(dfSummary(fire_data,
plain.ascii = FALSE,
style = "multiline",
headings = FALSE,
graph.magnif = 0.8,
valid.col = FALSE),
method = 'render')| No | Variable | Stats / Values | Freqs (% of Valid) | Graph | Missing | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | id [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 2 | al_number [integer] |
|
6836 distinct values |  |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 3 | al_location [character] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 4 | inc_borough [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 5 | zipcode [integer] |
|
210 distinct values |  |
2197 (6.7%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 6 | pol_prec [integer] |
|
77 distinct values |  |
2197 (6.7%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 7 | city_con_dist [integer] |
|
51 distinct values |  |
2197 (6.7%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 8 | commu_dist [integer] |
|
68 distinct values |  |
2197 (6.7%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 9 | commu_sc_dist [integer] |
|
32 distinct values |  |
2198 (6.7%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 10 | cong_dist [integer] |
|
13 distinct values |  |
2197 (6.7%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 11 | al_source_desc [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 12 | al_index_desc [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 13 | highest_al_level [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 14 | inc_class [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 15 | inc_class_group [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 16 | disp_resp_min_qy [numeric] |
|
198 distinct values |  |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 17 | first_ass_datetime [POSIXct, POSIXt] |
|
32747 distinct values |  |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 18 | first_act_datetime [POSIXct, POSIXt] |
|
32617 distinct values |  |
41 (0.1%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 19 | first_onscene_datetime [POSIXct, POSIXt] |
|
32679 distinct values |  |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 20 | inc_close_datetime [POSIXct, POSIXt] |
|
32681 distinct values |  |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 21 | inc_resp_min_indc [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 22 | inc_resp_min_qy [numeric] |
|
1181 distinct values |  |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 23 | inc_travel_min_qy [numeric] |
|
1157 distinct values |  |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 24 | engines_assigned [integer] |
|
15 distinct values |  |
4 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 25 | ladders_assigned [integer] |
|
12 distinct values |  |
4 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 26 | others_units_assigned [integer] |
|
22 distinct values |  |
4 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 27 | emergency_min_qy [numeric] |
|
4170 distinct values |  |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 28 | day_type [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 29 | ticket_time [numeric] |
|
4389 distinct values |  |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 30 | time_of_day [factor] |
|
|
 |
0 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 31 | total_assigned_unit [integer] |
|
34 distinct values |  |
4 (0.0%) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 32 | tua_is_one [factor] |
|
|
 |
4 (0.0%) |
Generated by summarytools 1.0.1 (R version 4.3.2)
2024-01-14
3.3 Additional Data Visaulization
In this section we will have a look on additional data visualisation in order to better understand how the predictors behaves.
summary(fire_data_new)## inc_borough al_source_desc al_index_desc
## Bronx :6406 PHONE :13465 DEFAULT RECORD: 2979
## Brooklyn :9280 EMS : 7369 Initial Alarm :27631
## Manhattan :7294 EMS-911: 4349 Others : 118
## Queens :6188 CLASS-3: 4817
## Staten Island:1560 Others : 728
##
## highest_al_level inc_class_group disp_resp_min_qy
## All Hands Working: 94 Medical Emergencies :11222 Min. : 0.03333
## First Alarm :30626 Medical MFAs : 146 1st Qu.: 0.13333
## 2nd-3rd Alarm : 8 NonMedical Emergencies:16471 Median : 0.48333
## NonMedical MFAs : 904 Mean : 0.50062
## NonStructural Fires : 547 3rd Qu.: 0.71667
## Structural Fires : 1438 Max. :34.73333
## inc_resp_min_qy inc_travel_min_qy engines_assigned ladders_assigned
## Min. : 0.350 Min. : 0.000 Min. : 0.000 Min. : 0.0000
## 1st Qu.: 4.383 1st Qu.: 3.883 1st Qu.: 1.000 1st Qu.: 0.0000
## Median : 5.467 Median : 4.983 Median : 1.000 Median : 1.0000
## Mean : 5.949 Mean : 5.448 Mean : 1.146 Mean : 0.7795
## 3rd Qu.: 6.850 3rd Qu.: 6.367 3rd Qu.: 1.000 3rd Qu.: 1.0000
## Max. :58.917 Max. :58.617 Max. :19.000 Max. :15.0000
## others_units_assigned emergency_min_qy day_type ticket_time
## Min. : 0.0000 Min. : 0.00 Weekday:22379 Min. : 1.083
## 1st Qu.: 0.0000 1st Qu.: 7.15 Weekend: 8349 1st Qu.: 12.850
## Median : 0.0000 Median : 11.93 Median : 17.900
## Mean : 0.3899 Mean : 17.08 Mean : 23.027
## 3rd Qu.: 1.0000 3rd Qu.: 19.58 3rd Qu.: 25.954
## Max. :32.0000 Max. :596.38 Max. :601.717
## time_of_day total_assigned_unit tua_is_one
## Night : 4487 Min. : 1.000 N:12940
## Morning : 8370 1st Qu.: 1.000 Y:17788
## Afternoon:10627 Median : 1.000
## Evening : 7244 Mean : 2.316
## 3rd Qu.: 3.000
## Max. :66.0003.3.1 Y value: inc_resp_min_qy
ggplot(fire_data_new,
aes(x = al_source_desc, y = inc_resp_min_qy, color = inc_class_group)) +
geom_boxplot() +
labs(title = "Alarm Source Description - Incident Minutes Response Time - Incident Class Borough",
x = "Alarm Source Description", y = "Incident Minutes Response Time", color = "Incident Class\nBorough")
Here we can see that for the EMS-911 alarm source only Medical Emergencis, Medical MFAs and NonMedical Emergencies were arrived. Moreover NonMedical Emergencies comes most from phone, whereas Medical Emergencies from EMS.
ggplot(fire_data_new,
aes(x = day_type, y = inc_resp_min_qy, color = inc_class_group)) +
geom_boxplot() +
labs(title = "Day Type - Incident Minutes Response Time - Incident Class Group",
x = "Day Type", y = "Incident Minutes Response Time", color = "Incident Class\nGroup")
In this boxplot we approximately can’t see any pattern for both day type and borough, whoever there are many outliers for medical and non medical emergencies since are the two predominant incident class.
ggplot(fire_data_new,
aes(x = time_of_day, y = inc_resp_min_qy, color = inc_class_group)) +
geom_boxplot() +
labs(title = "Day Range Time - Incident Minutes Response Time - Incident Class Group",
x = "Day Range Time", y = "Incident Minutes Response Time", color = "Incident Class\nGroup")
Simillarly as the previous described boxpolt here there we can’t see any particular relevant pattern.
ggplot(fire_data_new, aes(x = total_assigned_unit, y = inc_resp_min_qy, group = inc_class_group)) +
geom_point(aes(color = inc_class_group)) +
labs(title = "Total Assagned Units - Incident Minutes Response Time - Incident Class Group",
x = "Total Assagned Units", y = "Incident Minutes Response Time", color = "Incident Class\nGroup")
Whereas here as described in a previous similar chart, the total assigned units and the incident response time in minutes appear to be inversely proportional, with the contradistinction of structural fires that have many assigned units and low response time and Non Medical Emergencies that have low assigned units and high response time.
3.3.2 Y value: emergency_min_qy
Now we analyse the same box plot of before but now with a different response for the Y axis the emergency time in minutes.
ggplot(fire_data_new,
aes(x = al_source_desc, y = emergency_min_qy, color = inc_class_group)) +
geom_boxplot() +
labs(title = "Alarm Source Description - Emergency Minutes Time - Incident Borough",
x = "Alarm Source Description", y = "Emergency Minutes Time", color = "Incident Borough")
Here the first effect that we see is the high number of Structural Fires that are outside the fourth band for the phone alarm source description.
ggplot(fire_data_new,
aes(x = day_type, y = emergency_min_qy, color = inc_class_group)) +
geom_boxplot() +
labs(title = "Day Type - Emergency Minutes Time - Incident Class Group",
x = "Day Type", y = "Emergency Minutes Time", color = "Incident Class\nGroup")
Here instead we can’t see any pattern regarding day type, whereas we can see that the most outliers are from Structurl Fires in both day types.
ggplot(fire_data_new,
aes(x = time_of_day, y = emergency_min_qy, color = inc_class_group)) +
geom_boxplot() +
labs(title = "Day Range Time - Emergency Minutes Time - Incident Class Group",
x = "Day Range Time", y = "Emergency Minutes Time", color = "Incident Class\nGroup")
Again similar as the previous boxplots we can’t see any relevant patterns, except that the heavy outliers belonging to Structural Fires.
ggplot(fire_data_new, aes(x=total_assigned_unit, y=emergency_min_qy, group=inc_class_group)) +
geom_point(aes(color=inc_class_group)) +
labs(title = "Total Assagned Units - Emergency Minutes Time - Incident Class Group",
x = "Total Assagned Units", y = "Emergency Minutes Time", color = "Incident Class\nGroup")
Finally here we can see that the Structural Fire incident have lots of variance directly and seems be a directly proportional relationship between the total assigned units and the Emergency Time. For the NonMedical Emergencies they are clustered and then for the Medical Emergencies we can see that they have been mostly assigend a single units.
3.3.3 Maps Visualization
In this section we plot additional data visualization focus on the geographical visualization of the New York borough with relative predictors. In order to do so we load an additional datasets:
The fdny-firehouse-listing.csv is a dataset that includes the geographical informations of every firefighter stations in the NYC, including again latitude and longitude.
firefighter_stations <- read.csv("datasets/fdny-firehouse-listing.csv")
head(firefighter_stations)## FacilityName FacilityAddress
## 1 Engine 4/Ladder 15 42 South Street
## 2 Engine 10/Ladder 10 124 Liberty Street
## 3 Engine 6 49 Beekman Street
## 4 Engine 7/Ladder 1/Battalion 1/Manhattan Borough Command 100-104 Duane Street
## 5 Ladder 8 14 North Moore Street
## 6 Engine 9/Ladder 6 75 Canal Street
## Borough Postcode Latitude Longitude Community.Board Community.Council
## 1 Manhattan 10005 40.70347 -74.00754 1 1
## 2 Manhattan 10006 40.71007 -74.01252 1 1
## 3 Manhattan 10038 40.71005 -74.00525 1 1
## 4 Manhattan 10007 40.71546 -74.00594 1 1
## 5 Manhattan 10013 40.71976 -74.00668 1 1
## 6 Manhattan 10002 40.71521 -73.99290 3 1
## Census.Tract BIN BBL
## 1 7 1000867 1000350001
## 2 13 1075700 1000520022
## 3 1501 1001287 1000930030
## 4 33 1001647 1001500025
## 5 33 1002150 1001890035
## 6 16 1003898 1003000030
## NTA
## 1 Battery Park City-Lower Manhattan
## 2 Battery Park City-Lower Manhattan
## 3 Battery Park City-Lower Manhattan
## 4 SoHo-TriBeCa-Civic Center-Little Italy
## 5 SoHo-TriBeCa-Civic Center-Little Italy
## 6 Chinatownsummary(firefighter_stations)## FacilityName FacilityAddress Borough Postcode
## Length:218 Length:218 Length:218 Min. :10001
## Class :character Class :character Class :character 1st Qu.:10304
## Mode :character Mode :character Mode :character Median :11103
## Mean :10784
## 3rd Qu.:11231
## Max. :11695
## NA's :5
## Latitude Longitude Community.Board Community.Council
## Min. :40.51 Min. :-74.24 Min. : 1.000 Min. : 1.00
## 1st Qu.:40.66 1st Qu.:-73.99 1st Qu.: 3.000 1st Qu.:12.00
## Median :40.72 Median :-73.94 Median : 6.000 Median :27.00
## Mean :40.72 Mean :-73.94 Mean : 7.075 Mean :25.63
## 3rd Qu.:40.77 3rd Qu.:-73.89 3rd Qu.:11.000 3rd Qu.:38.00
## Max. :40.89 Max. :-73.72 Max. :84.000 Max. :51.00
## NA's :5 NA's :5 NA's :5 NA's :5
## Census.Tract BIN BBL NTA
## Min. : 1 Min. :1000867 Min. :1.000e+09 Length:218
## 1st Qu.: 129 1st Qu.:2003268 1st Qu.:2.025e+09 Class :character
## Median : 275 Median :3064786 Median :3.025e+09 Mode :character
## Mean : 5950 Mean :2900421 Mean :2.850e+09
## 3rd Qu.: 800 3rd Qu.:4090228 3rd Qu.:4.033e+09
## Max. :157902 Max. :5154879 Max. :5.080e+09
## NA's :5 NA's :5 NA's :5We now start with the firefighter stations dataset. By first making a copy of the fire_data_new and setting the borough from the firefighter_stations dataset to factor in order to be easily merged with the copied fire_data dataset.
# make a copy of the fire_data
fire_data_for_ffs <- fire_data_new
fire_data_for_ffs <- fire_data_for_ffs %>% rename(borough = inc_borough)
firefighter_stations$Borough <- as.factor(firefighter_stations$Borough)
firefighter_stations <- firefighter_stations %>% rename(borough = Borough)
# remove the na values from firefighter_stations
firefighter_stations <- na.omit(firefighter_stations)Now we want to get the number of firefighter station for each borough.
stations_borough <- firefighter_stations %>%
group_by(borough) %>%
summarise(number_of_stations = n())Now we want to get a summary of the incident count, the number of station and the incident per station of each borough in order to have a general view of the New York City situation.
count_inc_brough <- fire_data_for_ffs %>% group_by(borough) %>% summarise(incident_count = n())
stations_borough$incident_per_station <- round(count_inc_brough$incident_count / stations_borough$number_of_stations, digits = 3)
count_inc_brough <- merge(count_inc_brough, stations_borough, by="borough")
count_inc_brough## borough incident_count number_of_stations incident_per_station
## 1 Bronx 6406 34 188.412
## 2 Brooklyn 9280 64 145.000
## 3 Manhattan 7294 47 155.191
## 4 Queens 6188 48 128.917
## 5 Staten Island 1560 20 78.000Now we convert the firefighter_station data frame into a Spartial Data Frame to contains the geometry points.
firefighter_stations_sdf <- st_as_sf(firefighter_stations, coords = c("Longitude", "Latitude"), crs = 4326)
head(firefighter_stations_sdf)## Simple feature collection with 6 features and 10 fields
## Geometry type: POINT
## Dimension: XY
## Bounding box: xmin: -74.01252 ymin: 40.70347 xmax: -73.9929 ymax: 40.71976
## Geodetic CRS: WGS 84
## FacilityName FacilityAddress
## 1 Engine 4/Ladder 15 42 South Street
## 2 Engine 10/Ladder 10 124 Liberty Street
## 3 Engine 6 49 Beekman Street
## 4 Engine 7/Ladder 1/Battalion 1/Manhattan Borough Command 100-104 Duane Street
## 5 Ladder 8 14 North Moore Street
## 6 Engine 9/Ladder 6 75 Canal Street
## borough Postcode Community.Board Community.Council Census.Tract BIN
## 1 Manhattan 10005 1 1 7 1000867
## 2 Manhattan 10006 1 1 13 1075700
## 3 Manhattan 10038 1 1 1501 1001287
## 4 Manhattan 10007 1 1 33 1001647
## 5 Manhattan 10013 1 1 33 1002150
## 6 Manhattan 10002 3 1 16 1003898
## BBL
## 1 1000350001
## 2 1000520022
## 3 1000930030
## 4 1001500025
## 5 1001890035
## 6 1003000030
## NTA
## 1 Battery Park City-Lower Manhattan
## 2 Battery Park City-Lower Manhattan
## 3 Battery Park City-Lower Manhattan
## 4 SoHo-TriBeCa-Civic Center-Little Italy
## 5 SoHo-TriBeCa-Civic Center-Little Italy
## 6 Chinatown
## geometry
## 1 POINT (-74.00754 40.70347)
## 2 POINT (-74.01252 40.71007)
## 3 POINT (-74.00525 40.71005)
## 4 POINT (-74.00594 40.71546)
## 5 POINT (-74.00668 40.71976)
## 6 POINT (-73.9929 40.71521)3.3.3.1 Downloand of the geojson file
At this point we download the .geojson file that contain all the geometry of each borough in order to have a cool maps visualization of NYC.
geojson_newyork <- geojson_read("datasets/NYC_BoroughBoundaries.geojson", what = "sp")
geojson_newyork <- setNames(geojson_newyork, c("borough_code", "borough", "shape_area", "shape_leng"))
geojson_newyork$borough <- as.factor(geojson_newyork$borough)
geojson_newyork$borough_code <- NULL
head(geojson_newyork)## borough shape_area shape_leng
## 1 Staten Island 1623620725.05 325917.35395
## 2 Manhattan 636520502.758 357713.308162
## 3 Bronx 1187174772.5 463180.579449
## 4 Brooklyn 1934138215.76 728146.574928
## 5 Queens 3041418506.64 888199.731385And now we merge geojson_newyork with count_inc_brough maintaining the Spartial Data Frame type.
geojson_newyork@data = data.frame(geojson_newyork@data, count_inc_brough[match(geojson_newyork@data$borough, count_inc_brough$borough),])
geojson_newyork@data$borough.1 <- NULLAnd finally we can plot the interactive map using the mapview function.
mapview(list(firefighter_stations_sdf, geojson_newyork),
zcol = list(NULL, "incident_count"),
legend = list(FALSE, TRUE),
homebutton = list(FALSE, TRUE), layer.name = list(NULL, "indicents_number"), alpha.regions = 0.5, aplha = 1)4 Let’s build some models (or at least try)
As suggested by the professor we have opted to solve a regression problem with response first inc_resp_min_qy, and then the emergency_min_qy. Initially we were thinking to solve a multi-classification / binary classification problem for the inc_class_group, however we were considering all the time difference predictors that are a future information w.r.t. the inc_class_group in prediction time, so it doesn’t make much sense to use them, and it is possible also that they will result in super predictors. That’s way we decided to grab the professor suggestion.
For both analysis we transform the relative response in log scale in order to simulate the behaviour of the Exponential and Gamma GLMs.
So first things first let’s check if there are some observations that have at least one of the time differences equal to zero.
summary(fire_data_new %>% select(disp_resp_min_qy, inc_travel_min_qy, inc_resp_min_qy, emergency_min_qy, ticket_time))## disp_resp_min_qy inc_travel_min_qy inc_resp_min_qy emergency_min_qy
## Min. : 0.03333 Min. : 0.000 Min. : 0.350 Min. : 0.00
## 1st Qu.: 0.13333 1st Qu.: 3.883 1st Qu.: 4.383 1st Qu.: 7.15
## Median : 0.48333 Median : 4.983 Median : 5.467 Median : 11.93
## Mean : 0.50062 Mean : 5.448 Mean : 5.949 Mean : 17.08
## 3rd Qu.: 0.71667 3rd Qu.: 6.367 3rd Qu.: 6.850 3rd Qu.: 19.58
## Max. :34.73333 Max. :58.617 Max. :58.917 Max. :596.38
## ticket_time
## Min. : 1.083
## 1st Qu.: 12.850
## Median : 17.900
## Mean : 23.027
## 3rd Qu.: 25.954
## Max. :601.717fire_data_new <- fire_data_new %>% filter(inc_travel_min_qy != 0, emergency_min_qy != 0)Then we have to check the presence of correlation in the continuous predictor and if so deleting one or more of them.
round(cor(fire_data_new %>% dplyr::select(where(is.numeric)))^2, digits=3)## disp_resp_min_qy inc_resp_min_qy inc_travel_min_qy
## disp_resp_min_qy 1.000 0.018 0.003
## inc_resp_min_qy 0.018 1.000 0.967
## inc_travel_min_qy 0.003 0.967 1.000
## engines_assigned 0.011 0.064 0.075
## ladders_assigned 0.163 0.015 0.039
## others_units_assigned 0.025 0.023 0.033
## emergency_min_qy 0.002 0.000 0.000
## ticket_time 0.001 0.016 0.018
## total_assigned_unit 0.065 0.045 0.068
## engines_assigned ladders_assigned others_units_assigned
## disp_resp_min_qy 0.011 0.163 0.025
## inc_resp_min_qy 0.064 0.015 0.023
## inc_travel_min_qy 0.075 0.039 0.033
## engines_assigned 1.000 0.317 0.295
## ladders_assigned 0.317 1.000 0.325
## others_units_assigned 0.295 0.325 1.000
## emergency_min_qy 0.046 0.017 0.121
## ticket_time 0.031 0.012 0.105
## total_assigned_unit 0.719 0.693 0.704
## emergency_min_qy ticket_time total_assigned_unit
## disp_resp_min_qy 0.002 0.001 0.065
## inc_resp_min_qy 0.000 0.016 0.045
## inc_travel_min_qy 0.000 0.018 0.068
## engines_assigned 0.046 0.031 0.719
## ladders_assigned 0.017 0.012 0.693
## others_units_assigned 0.121 0.105 0.704
## emergency_min_qy 1.000 0.981 0.077
## ticket_time 0.981 1.000 0.060
## total_assigned_unit 0.077 0.060 1.000As we can see total_assigned_unit is heavily correlated to the other counts since it is the sum of those, that’s we we decided to remove from the dataframe. Continuing we note also that lot’s of time difference are correlated to each other, whoever it is obvious since some of them include other smaller difference, these measures will be managed soon once we deal with the two type of analysis. We have done this step to remove singluarities for the future models.
fire_data_new <- fire_data_new %>% select(-c(total_assigned_unit))Next before creating any model have to split the cleaned dataset into train and test, with 0.8% of the whole dataset for the train set and the remaining 20% for the test set.
set.seed(43)
split <- sample.split(fire_data_new, SplitRatio = 0.8)
# Create training and testing sets
fire_data.train <- subset(fire_data_new, split == TRUE)
fire_data.test <- subset(fire_data_new, split == FALSE)
rownames(fire_data.train) <- NULL
rownames(fire_data.test) <- NULL
dim(fire_data.train)## [1] 23043 16dim(fire_data.test)## [1] 7682 164.1 Linear Regression???
4.1.1 Use inc_resp_min_qy as response
In this section we use inc_resp_min_qy as response, so we have to remove all the time difference predictors that are computed with one of the two datetime that comes after the incident datetime, so all the other except for our actual response.
# make a copy of the train and test
resp_min_fd.train <- fire_data.train
resp_min_fd.test <- fire_data.test
# remove the future time differences
resp_min_fd.train <- resp_min_fd.train %>% select(-c(disp_resp_min_qy, inc_travel_min_qy, emergency_min_qy, ticket_time))
resp_min_fd.test <- resp_min_fd.test %>% select(-c(disp_resp_min_qy, inc_travel_min_qy, emergency_min_qy, ticket_time))Let’s build our first Linear Regression Model
lm_irm_full <- lm(inc_resp_min_qy ~ ., data = resp_min_fd.train)
summary(lm_irm_full)##
## Call:
## lm(formula = inc_resp_min_qy ~ ., data = resp_min_fd.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.014 -1.359 -0.384 0.814 52.604
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.80348 0.91357 6.353 2.16e-10 ***
## inc_boroughBrooklyn -1.01049 0.04763 -21.216 < 2e-16 ***
## inc_boroughManhattan -0.14836 0.05048 -2.939 0.003296 **
## inc_boroughQueens -0.31298 0.05263 -5.947 2.77e-09 ***
## inc_boroughStaten Island -0.73366 0.08366 -8.769 < 2e-16 ***
## al_source_descEMS -0.21151 0.11172 -1.893 0.058356 .
## al_source_descEMS-911 -0.27526 0.11282 -2.440 0.014701 *
## al_source_descCLASS-3 0.08852 0.05590 1.584 0.113303
## al_source_descOthers -1.09849 0.11663 -9.419 < 2e-16 ***
## al_index_descInitial Alarm -0.21548 0.07336 -2.937 0.003315 **
## al_index_descOthers 1.46382 0.88917 1.646 0.099720 .
## highest_al_levelFirst Alarm 0.84831 0.90124 0.941 0.346576
## highest_al_level2nd-3rd Alarm 3.84181 1.23754 3.104 0.001909 **
## inc_class_groupMedical MFAs -0.01443 0.24796 -0.058 0.953585
## inc_class_groupNonMedical Emergencies 0.45755 0.10936 4.184 2.88e-05 ***
## inc_class_groupNonMedical MFAs 0.34701 0.15923 2.179 0.029316 *
## inc_class_groupNonStructural Fires -0.21984 0.16588 -1.325 0.185091
## inc_class_groupStructural Fires -0.03962 0.13924 -0.285 0.775974
## engines_assigned -0.46587 0.02833 -16.446 < 2e-16 ***
## ladders_assigned 0.14897 0.04505 3.306 0.000947 ***
## others_units_assigned -0.10067 0.03025 -3.328 0.000877 ***
## day_typeWeekend -0.19471 0.03763 -5.175 2.30e-07 ***
## time_of_dayMorning -0.18403 0.05436 -3.385 0.000712 ***
## time_of_dayAfternoon -0.37902 0.05232 -7.244 4.48e-13 ***
## time_of_dayEvening -0.65517 0.05577 -11.749 < 2e-16 ***
## tua_is_oneY 1.08088 0.06341 17.047 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.536 on 23017 degrees of freedom
## Multiple R-squared: 0.1209, Adjusted R-squared: 0.12
## F-statistic: 126.6 on 25 and 23017 DF, p-value: < 2.2e-16par(mfrow=c(2,2))
plot(lm_irm_full)
Now we have to see if the linearity assumption are met and thus if we can use a linear regression model for our analysis. 1. Residuals vs Fitted plot: here we can see if our residuals have a linear pattern and this is confermed by the straight horizontal red line. Even if,we have an higher amount of spreaded observations on the top of the red line. 2. Q-Q Residuals plot: in this plot called also quantile - quantile residual plot and tells us if the residuals are normally distributed or not. If they follows the 45 degrees dotted line we can say so otherwise as in our case we can’t say that are normally distributed, as we will see in much detail later. 3. Scaled-Location / Spread-Location plot: tells us if the residuals are equally spread across the predictors. This is the assessments of Homoscedasticity or equal variance. And we would like to see a sort of horizontal line, something more or less in this case. 4. Residuals VS Leverage plot: helps us to identify the influential points with the Cook’s distance, so points that have influence on the regression line. And if some point feed in the area delimited by the dotted lines those points will be assigned as influential. In our case we do not have any observations that satisfy what we have just saied.
qqPlot(residuals(lm_irm_full))
## [1] 11795 20875Much clearly the qqPlot tells that the data the residuals are not normally distributed indeed are heavily right skewed. Thus we can’t trust the p-values and the estimation of the coefficients.
residualPlots(lm_irm_full)
## Test stat Pr(>|Test stat|)
## inc_borough
## al_source_desc
## al_index_desc
## highest_al_level
## inc_class_group
## engines_assigned 6.5604 5.480e-11 ***
## ladders_assigned 5.5546 2.813e-08 ***
## others_units_assigned 4.5496 5.403e-06 ***
## day_type
## time_of_day
## tua_is_one
## Tukey test 6.3052 2.878e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Here instead we have a look of all plots of residuals vs predictors and again the plot of residuals vs fitted values that we already see.
Let’s have a look of the possible power transformation of the response.
powerTransform(lm_irm_full)## Estimated transformation parameter
## Y1
## 0.1012643The function powerTransform suggests to take the log-transformation of the response, we take the log transformation because the estimated value of lambda is close to zero.
lm_irm_full_upd <- update(lm_irm_full, log(inc_resp_min_qy) ~ .)
summary(lm_irm_full_upd)##
## Call:
## lm(formula = log(inc_resp_min_qy) ~ inc_borough + al_source_desc +
## al_index_desc + highest_al_level + inc_class_group + engines_assigned +
## ladders_assigned + others_units_assigned + day_type + time_of_day +
## tua_is_one, data = resp_min_fd.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.47374 -0.19977 -0.00464 0.19592 2.69052
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.7180302 0.1334082 12.878 < 2e-16
## inc_boroughBrooklyn -0.1770990 0.0069553 -25.463 < 2e-16
## inc_boroughManhattan -0.0373227 0.0073715 -5.063 4.16e-07
## inc_boroughQueens -0.0465490 0.0076855 -6.057 1.41e-09
## inc_boroughStaten Island -0.1199289 0.0122171 -9.816 < 2e-16
## al_source_descEMS -0.0203318 0.0163151 -1.246 0.212705
## al_source_descEMS-911 -0.0339945 0.0164747 -2.063 0.039083
## al_source_descCLASS-3 0.0399158 0.0081626 4.890 1.01e-06
## al_source_descOthers -0.4691826 0.0170311 -27.549 < 2e-16
## al_index_descInitial Alarm -0.0287322 0.0107130 -2.682 0.007324
## al_index_descOthers 0.1761202 0.1298452 1.356 0.174990
## highest_al_levelFirst Alarm 0.1361029 0.1316083 1.034 0.301076
## highest_al_level2nd-3rd Alarm 0.6022132 0.1807176 3.332 0.000863
## inc_class_groupMedical MFAs 0.0003317 0.0362090 0.009 0.992691
## inc_class_groupNonMedical Emergencies 0.0788922 0.0159704 4.940 7.87e-07
## inc_class_groupNonMedical MFAs 0.0574061 0.0232520 2.469 0.013562
## inc_class_groupNonStructural Fires -0.0250603 0.0242238 -1.035 0.300898
## inc_class_groupStructural Fires -0.0223811 0.0203328 -1.101 0.271024
## engines_assigned -0.0749646 0.0041366 -18.122 < 2e-16
## ladders_assigned 0.0104863 0.0065793 1.594 0.110990
## others_units_assigned -0.0075662 0.0044175 -1.713 0.086771
## day_typeWeekend -0.0251404 0.0054948 -4.575 4.78e-06
## time_of_dayMorning -0.0653316 0.0079380 -8.230 < 2e-16
## time_of_dayAfternoon -0.0905598 0.0076402 -11.853 < 2e-16
## time_of_dayEvening -0.1252760 0.0081434 -15.384 < 2e-16
## tua_is_oneY 0.1538454 0.0092591 16.616 < 2e-16
##
## (Intercept) ***
## inc_boroughBrooklyn ***
## inc_boroughManhattan ***
## inc_boroughQueens ***
## inc_boroughStaten Island ***
## al_source_descEMS
## al_source_descEMS-911 *
## al_source_descCLASS-3 ***
## al_source_descOthers ***
## al_index_descInitial Alarm **
## al_index_descOthers
## highest_al_levelFirst Alarm
## highest_al_level2nd-3rd Alarm ***
## inc_class_groupMedical MFAs
## inc_class_groupNonMedical Emergencies ***
## inc_class_groupNonMedical MFAs *
## inc_class_groupNonStructural Fires
## inc_class_groupStructural Fires
## engines_assigned ***
## ladders_assigned
## others_units_assigned .
## day_typeWeekend ***
## time_of_dayMorning ***
## time_of_dayAfternoon ***
## time_of_dayEvening ***
## tua_is_oneY ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3703 on 23017 degrees of freedom
## Multiple R-squared: 0.163, Adjusted R-squared: 0.162
## F-statistic: 179.2 on 25 and 23017 DF, p-value: < 2.2e-16Now remember that we can’t compere the \(R^2\) with the previous model since in the last one the response is on a different scale.
Let’s see how the residuals behaves in this new model.
par(mfrow=c(2,2))
plot(lm_irm_full_upd)
Like the previous model we can say the residuals follow a linear pattern much better that the previous model. Again we do not have any influential point. But on the other hand the qqPlot is pretty much a mess indicating that the residuals are not normally distributed, by this qqPlot we can say that:
- The smallest observations are larger than you would expect from a normal distribution (i.e. the points are above the line on the QQ-plot). This means the lower tail of the data’s distribution has been reduced, relative to a normal distribution.
- The largest observations are less than you would expect from a normal distribution (i.e. the points are below the line on the QQ-plot). This means the upper tail of the data’s distribution has been reduced, relative to a normal distribution.
The qqPlot is buch clear here, where we can see also the residuals vs predictors and residuals vs fitted values.
residualPlots(lm_irm_full_upd)
## Test stat Pr(>|Test stat|)
## inc_borough
## al_source_desc
## al_index_desc
## highest_al_level
## inc_class_group
## engines_assigned 5.5255 3.321e-08 ***
## ladders_assigned 5.1370 2.815e-07 ***
## others_units_assigned 4.4142 1.018e-05 ***
## day_type
## time_of_day
## tua_is_one
## Tukey test 6.1078 1.010e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1qqPlot(residuals(lm_irm_full_upd))
## [1] 8399 11439Thus again the linear assumptions are not meet, mainly by the non normal distribution of the residuals.
At this point we have decided in any case to investigate this behaviour trying to fix the non normality of the residuals by modifying the scale of some predictors and adding interaction term between them.
We start by modifying the previous model by adding the interaction term and scaling the numbe of assigned units by the logarithm scale after having increased by a single units.
lm_irm_full_upd_2 <- update(lm_irm_full_upd, log(inc_resp_min_qy) ~ . + engines_assigned : inc_class_group + time_of_day : day_type + log(ladders_assigned + 1) + log(engines_assigned + 1) + log(others_units_assigned + 1) + log(engines_assigned + 1) : inc_class_group)
summary(lm_irm_full_upd_2)##
## Call:
## lm(formula = log(inc_resp_min_qy) ~ inc_borough + al_source_desc +
## al_index_desc + highest_al_level + inc_class_group + engines_assigned +
## ladders_assigned + others_units_assigned + day_type + time_of_day +
## tua_is_one + log(ladders_assigned + 1) + log(engines_assigned +
## 1) + log(others_units_assigned + 1) + inc_class_group:engines_assigned +
## day_type:time_of_day + inc_class_group:log(engines_assigned +
## 1), data = resp_min_fd.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.67577 -0.19744 -0.00207 0.19826 2.55364
##
## Coefficients:
## Estimate
## (Intercept) 1.762201
## inc_boroughBrooklyn -0.179870
## inc_boroughManhattan -0.041988
## inc_boroughQueens -0.045810
## inc_boroughStaten Island -0.122447
## al_source_descEMS -0.026849
## al_source_descEMS-911 -0.041289
## al_source_descCLASS-3 0.032810
## al_source_descOthers -0.499088
## al_index_descInitial Alarm -0.030575
## al_index_descOthers -0.005135
## highest_al_levelFirst Alarm 0.120641
## highest_al_level2nd-3rd Alarm -0.924549
## inc_class_groupMedical MFAs -0.021754
## inc_class_groupNonMedical Emergencies 0.426759
## inc_class_groupNonMedical MFAs 0.574809
## inc_class_groupNonStructural Fires -0.064680
## inc_class_groupStructural Fires 0.383284
## engines_assigned -0.195436
## ladders_assigned 0.291426
## others_units_assigned 0.003291
## day_typeWeekend 0.002372
## time_of_dayMorning -0.054184
## time_of_dayAfternoon -0.081539
## time_of_dayEvening -0.130137
## tua_is_oneY -0.034157
## log(ladders_assigned + 1) -0.679472
## log(engines_assigned + 1) 0.419757
## log(others_units_assigned + 1) -0.049386
## inc_class_groupMedical MFAs:engines_assigned 0.123800
## inc_class_groupNonMedical Emergencies:engines_assigned 0.340628
## inc_class_groupNonMedical MFAs:engines_assigned 0.523430
## inc_class_groupNonStructural Fires:engines_assigned 0.161493
## inc_class_groupStructural Fires:engines_assigned 0.202559
## day_typeWeekend:time_of_dayMorning -0.053103
## day_typeWeekend:time_of_dayAfternoon -0.047725
## day_typeWeekend:time_of_dayEvening 0.013392
## inc_class_groupMedical MFAs:log(engines_assigned + 1) -0.158047
## inc_class_groupNonMedical Emergencies:log(engines_assigned + 1) -1.012682
## inc_class_groupNonMedical MFAs:log(engines_assigned + 1) -1.591994
## inc_class_groupNonStructural Fires:log(engines_assigned + 1) -0.286924
## inc_class_groupStructural Fires:log(engines_assigned + 1) -0.796810
## Std. Error
## (Intercept) 0.136218
## inc_boroughBrooklyn 0.006888
## inc_boroughManhattan 0.007297
## inc_boroughQueens 0.007616
## inc_boroughStaten Island 0.012097
## al_source_descEMS 0.016447
## al_source_descEMS-911 0.016576
## al_source_descCLASS-3 0.008296
## al_source_descOthers 0.016993
## al_index_descInitial Alarm 0.010597
## al_index_descOthers 0.137273
## highest_al_levelFirst Alarm 0.132032
## highest_al_level2nd-3rd Alarm 0.272628
## inc_class_groupMedical MFAs 0.164270
## inc_class_groupNonMedical Emergencies 0.028837
## inc_class_groupNonMedical MFAs 0.041492
## inc_class_groupNonStructural Fires 0.094043
## inc_class_groupStructural Fires 0.061241
## engines_assigned 0.075380
## ladders_assigned 0.026140
## others_units_assigned 0.009306
## day_typeWeekend 0.013525
## time_of_dayMorning 0.009375
## time_of_dayAfternoon 0.009052
## time_of_dayEvening 0.009666
## tua_is_oneY 0.014256
## log(ladders_assigned + 1) 0.050962
## log(engines_assigned + 1) 0.122205
## log(others_units_assigned + 1) 0.021401
## inc_class_groupMedical MFAs:engines_assigned 0.270299
## inc_class_groupNonMedical Emergencies:engines_assigned 0.076922
## inc_class_groupNonMedical MFAs:engines_assigned 0.090692
## inc_class_groupNonStructural Fires:engines_assigned 0.110614
## inc_class_groupStructural Fires:engines_assigned 0.083385
## day_typeWeekend:time_of_dayMorning 0.017182
## day_typeWeekend:time_of_dayAfternoon 0.016465
## day_typeWeekend:time_of_dayEvening 0.017479
## inc_class_groupMedical MFAs:log(engines_assigned + 1) 0.557364
## inc_class_groupNonMedical Emergencies:log(engines_assigned + 1) 0.128703
## inc_class_groupNonMedical MFAs:log(engines_assigned + 1) 0.171504
## inc_class_groupNonStructural Fires:log(engines_assigned + 1) 0.266366
## inc_class_groupStructural Fires:log(engines_assigned + 1) 0.168937
## t value
## (Intercept) 12.937
## inc_boroughBrooklyn -26.114
## inc_boroughManhattan -5.754
## inc_boroughQueens -6.015
## inc_boroughStaten Island -10.122
## al_source_descEMS -1.632
## al_source_descEMS-911 -2.491
## al_source_descCLASS-3 3.955
## al_source_descOthers -29.370
## al_index_descInitial Alarm -2.885
## al_index_descOthers -0.037
## highest_al_levelFirst Alarm 0.914
## highest_al_level2nd-3rd Alarm -3.391
## inc_class_groupMedical MFAs -0.132
## inc_class_groupNonMedical Emergencies 14.799
## inc_class_groupNonMedical MFAs 13.854
## inc_class_groupNonStructural Fires -0.688
## inc_class_groupStructural Fires 6.259
## engines_assigned -2.593
## ladders_assigned 11.149
## others_units_assigned 0.354
## day_typeWeekend 0.175
## time_of_dayMorning -5.780
## time_of_dayAfternoon -9.007
## time_of_dayEvening -13.463
## tua_is_oneY -2.396
## log(ladders_assigned + 1) -13.333
## log(engines_assigned + 1) 3.435
## log(others_units_assigned + 1) -2.308
## inc_class_groupMedical MFAs:engines_assigned 0.458
## inc_class_groupNonMedical Emergencies:engines_assigned 4.428
## inc_class_groupNonMedical MFAs:engines_assigned 5.772
## inc_class_groupNonStructural Fires:engines_assigned 1.460
## inc_class_groupStructural Fires:engines_assigned 2.429
## day_typeWeekend:time_of_dayMorning -3.091
## day_typeWeekend:time_of_dayAfternoon -2.899
## day_typeWeekend:time_of_dayEvening 0.766
## inc_class_groupMedical MFAs:log(engines_assigned + 1) -0.284
## inc_class_groupNonMedical Emergencies:log(engines_assigned + 1) -7.868
## inc_class_groupNonMedical MFAs:log(engines_assigned + 1) -9.283
## inc_class_groupNonStructural Fires:log(engines_assigned + 1) -1.077
## inc_class_groupStructural Fires:log(engines_assigned + 1) -4.717
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## inc_boroughBrooklyn < 2e-16 ***
## inc_boroughManhattan 8.82e-09 ***
## inc_boroughQueens 1.83e-09 ***
## inc_boroughStaten Island < 2e-16 ***
## al_source_descEMS 0.102593
## al_source_descEMS-911 0.012751 *
## al_source_descCLASS-3 7.67e-05 ***
## al_source_descOthers < 2e-16 ***
## al_index_descInitial Alarm 0.003915 **
## al_index_descOthers 0.970160
## highest_al_levelFirst Alarm 0.360871
## highest_al_level2nd-3rd Alarm 0.000697 ***
## inc_class_groupMedical MFAs 0.894646
## inc_class_groupNonMedical Emergencies < 2e-16 ***
## inc_class_groupNonMedical MFAs < 2e-16 ***
## inc_class_groupNonStructural Fires 0.491607
## inc_class_groupStructural Fires 3.95e-10 ***
## engines_assigned 0.009529 **
## ladders_assigned < 2e-16 ***
## others_units_assigned 0.723635
## day_typeWeekend 0.860810
## time_of_dayMorning 7.59e-09 ***
## time_of_dayAfternoon < 2e-16 ***
## time_of_dayEvening < 2e-16 ***
## tua_is_oneY 0.016581 *
## log(ladders_assigned + 1) < 2e-16 ***
## log(engines_assigned + 1) 0.000594 ***
## log(others_units_assigned + 1) 0.021028 *
## inc_class_groupMedical MFAs:engines_assigned 0.646947
## inc_class_groupNonMedical Emergencies:engines_assigned 9.54e-06 ***
## inc_class_groupNonMedical MFAs:engines_assigned 7.96e-09 ***
## inc_class_groupNonStructural Fires:engines_assigned 0.144310
## inc_class_groupStructural Fires:engines_assigned 0.015139 *
## day_typeWeekend:time_of_dayMorning 0.001999 **
## day_typeWeekend:time_of_dayAfternoon 0.003753 **
## day_typeWeekend:time_of_dayEvening 0.443572
## inc_class_groupMedical MFAs:log(engines_assigned + 1) 0.776748
## inc_class_groupNonMedical Emergencies:log(engines_assigned + 1) 3.75e-15 ***
## inc_class_groupNonMedical MFAs:log(engines_assigned + 1) < 2e-16 ***
## inc_class_groupNonStructural Fires:log(engines_assigned + 1) 0.281410
## inc_class_groupStructural Fires:log(engines_assigned + 1) 2.41e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3661 on 23001 degrees of freedom
## Multiple R-squared: 0.1825, Adjusted R-squared: 0.1811
## F-statistic: 125.3 on 41 and 23001 DF, p-value: < 2.2e-16par(mfrow=c(2,2))
plot(lm_irm_full_upd_2)
residualPlots(lm_irm_full_upd_2)
## Test stat Pr(>|Test stat|)
## inc_borough
## al_source_desc
## al_index_desc
## highest_al_level
## inc_class_group
## engines_assigned -6.0990 1.084e-09 ***
## ladders_assigned -6.8003 1.070e-11 ***
## others_units_assigned -4.5106 6.497e-06 ***
## day_type
## time_of_day
## tua_is_one
## log(ladders_assigned + 1) 8.6788 < 2.2e-16 ***
## log(engines_assigned + 1) 9.5963 < 2.2e-16 ***
## log(others_units_assigned + 1) 4.9674 6.833e-07 ***
## Tukey test 2.5600 0.01047 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1influenceIndexPlot(lm_irm_full_upd_2, vars = "Cook")
Again we it seems that nothing have changed regarding the qqPlot, whereas the distribution of fitted - residuals values is a little bit spreaded randomly. However here we have not constant variance on the residuals and we have also an influential point the 9504.
Let’s see the influential point and check how it behaves.
resp_min_fd.train[9504,]## inc_borough al_source_desc al_index_desc highest_al_level inc_class_group
## 9504 Bronx EMS-911 DEFAULT RECORD First Alarm Medical MFAs
## inc_resp_min_qy engines_assigned ladders_assigned others_units_assigned
## 9504 4.516667 4 3 15
## day_type time_of_day tua_is_one
## 9504 Weekday Evening NNow we investigate on why the 10036 observation is an influential point. Let’s see how is the behaviour of the logarithm scale of the assigned units for the Structural Fire and see if we can find the observation 9504.
infl_point <- subset(resp_min_fd.train, inc_class_group == "Medical MFAs")
# Create a boxplot for Engines Assigned
p1 <- ggplot(infl_point, aes(y = log(engines_assigned + 1))) +
geom_boxplot() +
ggtitle("Engines Assigned") +
geom_point(aes(x = 0, y = log(resp_min_fd.train[9504, "engines_assigned"] + 1)), col = "red", pch = 16) +
labs(title = "Engines Units Count",
x = "Engines Units", y = "Count")
# Create a boxplot for Ladders Assigned
p2 <-ggplot(infl_point, aes(y = log(ladders_assigned + 1))) +
geom_boxplot() +
ggtitle("Ladders Assigned") +
geom_point(aes(x = 0, y = log(resp_min_fd.train[9504, "ladders_assigned"] + 1)), col = "red", pch = 16) +
labs(title = "Ladders Units Count",
x = "Ladders Units", y = "Count")
# Create a boxplot for Other Units Assigned
p3 <- ggplot(infl_point, aes(y = log(others_units_assigned + 1))) +
geom_boxplot() +
ggtitle("Other Units Assigned") +
geom_point(aes(x = 0, y = log(resp_min_fd.train[9504, "others_units_assigned"] + 1)), col = "red", pch = 16) +
labs(title = "Other Units Count",
x = "Other Units", y = "Count")
# Display the plots in a 1x3 grid
grid.arrange(p1, p2, p3, ncol = 3)
And we see that the observed incident is far away from the distribution of others assigned units for the Medical MFAs incident, so we decide to remove this observation during the refitting of the last model.
lm_irm_full_upd_3 <- update(lm_irm_full_upd_2, subset = -9504)
summary(lm_irm_full_upd_3)##
## Call:
## lm(formula = log(inc_resp_min_qy) ~ inc_borough + al_source_desc +
## al_index_desc + highest_al_level + inc_class_group + engines_assigned +
## ladders_assigned + others_units_assigned + day_type + time_of_day +
## tua_is_one + log(ladders_assigned + 1) + log(engines_assigned +
## 1) + log(others_units_assigned + 1) + inc_class_group:engines_assigned +
## day_type:time_of_day + inc_class_group:log(engines_assigned +
## 1), data = resp_min_fd.train, subset = -9504)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.67539 -0.19761 -0.00197 0.19814 2.55387
##
## Coefficients:
## Estimate
## (Intercept) 1.764847
## inc_boroughBrooklyn -0.179775
## inc_boroughManhattan -0.041868
## inc_boroughQueens -0.045725
## inc_boroughStaten Island -0.122401
## al_source_descEMS -0.027197
## al_source_descEMS-911 -0.041425
## al_source_descCLASS-3 0.032895
## al_source_descOthers -0.499213
## al_index_descInitial Alarm -0.030541
## al_index_descOthers -0.010355
## highest_al_levelFirst Alarm 0.118423
## highest_al_level2nd-3rd Alarm -0.931039
## inc_class_groupMedical MFAs 0.012071
## inc_class_groupNonMedical Emergencies 0.426243
## inc_class_groupNonMedical MFAs 0.574323
## inc_class_groupNonStructural Fires -0.065413
## inc_class_groupStructural Fires 0.381807
## engines_assigned -0.195615
## ladders_assigned 0.290993
## others_units_assigned 0.004452
## day_typeWeekend 0.002383
## time_of_dayMorning -0.054215
## time_of_dayAfternoon -0.081532
## time_of_dayEvening -0.130086
## tua_is_oneY -0.034017
## log(ladders_assigned + 1) -0.679023
## log(engines_assigned + 1) 0.419479
## log(others_units_assigned + 1) -0.051644
## inc_class_groupMedical MFAs:engines_assigned 1.770697
## inc_class_groupNonMedical Emergencies:engines_assigned 0.340976
## inc_class_groupNonMedical MFAs:engines_assigned 0.524001
## inc_class_groupNonStructural Fires:engines_assigned 0.162001
## inc_class_groupStructural Fires:engines_assigned 0.201971
## day_typeWeekend:time_of_dayMorning -0.053080
## day_typeWeekend:time_of_dayAfternoon -0.048092
## day_typeWeekend:time_of_dayEvening 0.013318
## inc_class_groupMedical MFAs:log(engines_assigned + 1) -2.591759
## inc_class_groupNonMedical Emergencies:log(engines_assigned + 1) -1.012281
## inc_class_groupNonMedical MFAs:log(engines_assigned + 1) -1.592082
## inc_class_groupNonStructural Fires:log(engines_assigned + 1) -0.286766
## inc_class_groupStructural Fires:log(engines_assigned + 1) -0.793631
## Std. Error
## (Intercept) 0.136218
## inc_boroughBrooklyn 0.006888
## inc_boroughManhattan 0.007297
## inc_boroughQueens 0.007616
## inc_boroughStaten Island 0.012096
## al_source_descEMS 0.016447
## al_source_descEMS-911 0.016576
## al_source_descCLASS-3 0.008295
## al_source_descOthers 0.016992
## al_index_descInitial Alarm 0.010596
## al_index_descOthers 0.137295
## highest_al_levelFirst Alarm 0.132030
## highest_al_level2nd-3rd Alarm 0.272636
## inc_class_groupMedical MFAs 0.165264
## inc_class_groupNonMedical Emergencies 0.028837
## inc_class_groupNonMedical MFAs 0.041490
## inc_class_groupNonStructural Fires 0.094039
## inc_class_groupStructural Fires 0.061243
## engines_assigned 0.075376
## ladders_assigned 0.026140
## others_units_assigned 0.009326
## day_typeWeekend 0.013525
## time_of_dayMorning 0.009375
## time_of_dayAfternoon 0.009052
## time_of_dayEvening 0.009666
## tua_is_oneY 0.014255
## log(ladders_assigned + 1) 0.050960
## log(engines_assigned + 1) 0.122198
## log(others_units_assigned + 1) 0.021434
## inc_class_groupMedical MFAs:engines_assigned 0.925465
## inc_class_groupNonMedical Emergencies:engines_assigned 0.076918
## inc_class_groupNonMedical MFAs:engines_assigned 0.090688
## inc_class_groupNonStructural Fires:engines_assigned 0.110608
## inc_class_groupStructural Fires:engines_assigned 0.083381
## day_typeWeekend:time_of_dayMorning 0.017181
## day_typeWeekend:time_of_dayAfternoon 0.016466
## day_typeWeekend:time_of_dayEvening 0.017478
## inc_class_groupMedical MFAs:log(engines_assigned + 1) 1.421777
## inc_class_groupNonMedical Emergencies:log(engines_assigned + 1) 0.128696
## inc_class_groupNonMedical MFAs:log(engines_assigned + 1) 0.171494
## inc_class_groupNonStructural Fires:log(engines_assigned + 1) 0.266352
## inc_class_groupStructural Fires:log(engines_assigned + 1) 0.168937
## t value
## (Intercept) 12.956
## inc_boroughBrooklyn -26.101
## inc_boroughManhattan -5.738
## inc_boroughQueens -6.004
## inc_boroughStaten Island -10.119
## al_source_descEMS -1.654
## al_source_descEMS-911 -2.499
## al_source_descCLASS-3 3.965
## al_source_descOthers -29.379
## al_index_descInitial Alarm -2.882
## al_index_descOthers -0.075
## highest_al_levelFirst Alarm 0.897
## highest_al_level2nd-3rd Alarm -3.415
## inc_class_groupMedical MFAs 0.073
## inc_class_groupNonMedical Emergencies 14.781
## inc_class_groupNonMedical MFAs 13.842
## inc_class_groupNonStructural Fires -0.696
## inc_class_groupStructural Fires 6.234
## engines_assigned -2.595
## ladders_assigned 11.132
## others_units_assigned 0.477
## day_typeWeekend 0.176
## time_of_dayMorning -5.783
## time_of_dayAfternoon -9.007
## time_of_dayEvening -13.459
## tua_is_oneY -2.386
## log(ladders_assigned + 1) -13.325
## log(engines_assigned + 1) 3.433
## log(others_units_assigned + 1) -2.409
## inc_class_groupMedical MFAs:engines_assigned 1.913
## inc_class_groupNonMedical Emergencies:engines_assigned 4.433
## inc_class_groupNonMedical MFAs:engines_assigned 5.778
## inc_class_groupNonStructural Fires:engines_assigned 1.465
## inc_class_groupStructural Fires:engines_assigned 2.422
## day_typeWeekend:time_of_dayMorning -3.090
## day_typeWeekend:time_of_dayAfternoon -2.921
## day_typeWeekend:time_of_dayEvening 0.762
## inc_class_groupMedical MFAs:log(engines_assigned + 1) -1.823
## inc_class_groupNonMedical Emergencies:log(engines_assigned + 1) -7.866
## inc_class_groupNonMedical MFAs:log(engines_assigned + 1) -9.284
## inc_class_groupNonStructural Fires:log(engines_assigned + 1) -1.077
## inc_class_groupStructural Fires:log(engines_assigned + 1) -4.698
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## inc_boroughBrooklyn < 2e-16 ***
## inc_boroughManhattan 9.71e-09 ***
## inc_boroughQueens 1.95e-09 ***
## inc_boroughStaten Island < 2e-16 ***
## al_source_descEMS 0.098212 .
## al_source_descEMS-911 0.012455 *
## al_source_descCLASS-3 7.35e-05 ***
## al_source_descOthers < 2e-16 ***
## al_index_descInitial Alarm 0.003953 **
## al_index_descOthers 0.939882
## highest_al_levelFirst Alarm 0.369762
## highest_al_level2nd-3rd Alarm 0.000639 ***
## inc_class_groupMedical MFAs 0.941776
## inc_class_groupNonMedical Emergencies < 2e-16 ***
## inc_class_groupNonMedical MFAs < 2e-16 ***
## inc_class_groupNonStructural Fires 0.486694
## inc_class_groupStructural Fires 4.62e-10 ***
## engines_assigned 0.009460 **
## ladders_assigned < 2e-16 ***
## others_units_assigned 0.633126
## day_typeWeekend 0.860151
## time_of_dayMorning 7.42e-09 ***
## time_of_dayAfternoon < 2e-16 ***
## time_of_dayEvening < 2e-16 ***
## tua_is_oneY 0.017025 *
## log(ladders_assigned + 1) < 2e-16 ***
## log(engines_assigned + 1) 0.000598 ***
## log(others_units_assigned + 1) 0.015986 *
## inc_class_groupMedical MFAs:engines_assigned 0.055721 .
## inc_class_groupNonMedical Emergencies:engines_assigned 9.34e-06 ***
## inc_class_groupNonMedical MFAs:engines_assigned 7.65e-09 ***
## inc_class_groupNonStructural Fires:engines_assigned 0.143033
## inc_class_groupStructural Fires:engines_assigned 0.015432 *
## day_typeWeekend:time_of_dayMorning 0.002007 **
## day_typeWeekend:time_of_dayAfternoon 0.003495 **
## day_typeWeekend:time_of_dayEvening 0.446071
## inc_class_groupMedical MFAs:log(engines_assigned + 1) 0.068331 .
## inc_class_groupNonMedical Emergencies:log(engines_assigned + 1) 3.83e-15 ***
## inc_class_groupNonMedical MFAs:log(engines_assigned + 1) < 2e-16 ***
## inc_class_groupNonStructural Fires:log(engines_assigned + 1) 0.281650
## inc_class_groupStructural Fires:log(engines_assigned + 1) 2.65e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.366 on 23000 degrees of freedom
## Multiple R-squared: 0.1826, Adjusted R-squared: 0.1812
## F-statistic: 125.4 on 41 and 23000 DF, p-value: < 2.2e-16par(mfrow=c(2,2))
plot(lm_irm_full_upd_3)## Warning: non si riesce a fare il plot senza sfruttarne uno:
## 3682
Again we are on the same situation of before.
residualPlots(lm_irm_full_upd_3)
## Test stat Pr(>|Test stat|)
## inc_borough
## al_source_desc
## al_index_desc
## highest_al_level
## inc_class_group
## engines_assigned -6.1096 1.015e-09 ***
## ladders_assigned -6.8157 9.612e-12 ***
## others_units_assigned -4.4780 7.572e-06 ***
## day_type
## time_of_day
## tua_is_one
## log(ladders_assigned + 1) 8.6987 < 2.2e-16 ***
## log(engines_assigned + 1) 9.6015 < 2.2e-16 ***
## log(others_units_assigned + 1) 4.9321 8.194e-07 ***
## Tukey test 2.5757 0.01 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1qqPlot(residuals(lm_irm_full_upd_3))
## 11439 8399
## 11438 8399influenceIndexPlot(lm_irm_full_upd_3, vars = "Cook")
summary(fitted(lm_irm_full_upd_3))## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.6401 1.5997 1.7104 1.7008 1.8040 2.3946We try again to remove the influential point even if it is not outside the cook’s band.
resp_min_fd.train[16373,]## inc_borough al_source_desc al_index_desc highest_al_level
## 16373 Brooklyn PHONE Others 2nd-3rd Alarm
## inc_class_group inc_resp_min_qy engines_assigned ladders_assigned
## 16373 Structural Fires 2.916667 18 13
## others_units_assigned day_type time_of_day tua_is_one
## 16373 25 Weekend Night Ninfl_point <- subset(resp_min_fd.train, inc_class_group == "Structural Fires")
# Create a boxplot for Engines Assigned
p1 <- ggplot(infl_point, aes(y = log(engines_assigned + 1))) +
geom_boxplot() +
ggtitle("Engines Assigned") +
geom_point(aes(x = 0, y = log(resp_min_fd.train[16373, "engines_assigned"] + 1)), col = "red", pch = 16) +
labs(title = "Engines Units Count",
x = "Engines Units", y = "Count")
# Create a boxplot for Ladders Assigned
p2 <-ggplot(infl_point, aes(y = log(ladders_assigned + 1))) +
geom_boxplot() +
ggtitle("Ladders Assigned") +
geom_point(aes(x = 0, y = log(resp_min_fd.train[16373, "ladders_assigned"] + 1)), col = "red", pch = 16) +
labs(title = "Ladders Units Count",
x = "Ladders Units", y = "Count")
# Create a boxplot for Other Units Assigned
p3 <- ggplot(infl_point, aes(y = log(others_units_assigned + 1))) +
geom_boxplot() +
ggtitle("Other Units Assigned") +
geom_point(aes(x = 0, y = log(resp_min_fd.train[16373, "others_units_assigned"] + 1)), col = "red", pch = 16) +
labs(title = "Other Units Count",
x = "Other Units", y = "Count")
# Display the plots in a 1x3 grid
grid.arrange(p1, p2, p3, ncol = 3)
lm_irm_full_upd_4 <- update(lm_irm_full_upd_2, subset = -c(16373, 9504))
summary(lm_irm_full_upd_4)##
## Call:
## lm(formula = log(inc_resp_min_qy) ~ inc_borough + al_source_desc +
## al_index_desc + highest_al_level + inc_class_group + engines_assigned +
## ladders_assigned + others_units_assigned + day_type + time_of_day +
## tua_is_one + log(ladders_assigned + 1) + log(engines_assigned +
## 1) + log(others_units_assigned + 1) + inc_class_group:engines_assigned +
## day_type:time_of_day + inc_class_group:log(engines_assigned +
## 1), data = resp_min_fd.train, subset = -c(16373, 9504))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.67877 -0.19727 -0.00203 0.19841 2.55264
##
## Coefficients:
## Estimate
## (Intercept) 1.793425
## inc_boroughBrooklyn -0.179560
## inc_boroughManhattan -0.041922
## inc_boroughQueens -0.045695
## inc_boroughStaten Island -0.122824
## al_source_descEMS -0.027649
## al_source_descEMS-911 -0.041880
## al_source_descCLASS-3 0.033267
## al_source_descOthers -0.499566
## al_index_descInitial Alarm -0.030482
## al_index_descOthers -0.074398
## highest_al_levelFirst Alarm 0.093107
## highest_al_level2nd-3rd Alarm -0.976258
## inc_class_groupMedical MFAs 0.012376
## inc_class_groupNonMedical Emergencies 0.426807
## inc_class_groupNonMedical MFAs 0.574842
## inc_class_groupNonStructural Fires -0.065866
## inc_class_groupStructural Fires 0.434765
## engines_assigned -0.196669
## ladders_assigned 0.298768
## others_units_assigned 0.005543
## day_typeWeekend 0.003642
## time_of_dayMorning -0.054005
## time_of_dayAfternoon -0.081320
## time_of_dayEvening -0.129651
## tua_is_oneY -0.035994
## log(ladders_assigned + 1) -0.693855
## log(engines_assigned + 1) 0.419252
## log(others_units_assigned + 1) -0.054969
## inc_class_groupMedical MFAs:engines_assigned 1.773750
## inc_class_groupNonMedical Emergencies:engines_assigned 0.342424
## inc_class_groupNonMedical MFAs:engines_assigned 0.526156
## inc_class_groupNonStructural Fires:engines_assigned 0.163860
## inc_class_groupStructural Fires:engines_assigned 0.253909
## day_typeWeekend:time_of_dayMorning -0.054177
## day_typeWeekend:time_of_dayAfternoon -0.049276
## day_typeWeekend:time_of_dayEvening 0.011822
## inc_class_groupMedical MFAs:log(engines_assigned + 1) -2.596486
## inc_class_groupNonMedical Emergencies:log(engines_assigned + 1) -1.014810
## inc_class_groupNonMedical MFAs:log(engines_assigned + 1) -1.596092
## inc_class_groupNonStructural Fires:log(engines_assigned + 1) -0.289099
## inc_class_groupStructural Fires:log(engines_assigned + 1) -0.946323
## Std. Error
## (Intercept) 0.136505
## inc_boroughBrooklyn 0.006887
## inc_boroughManhattan 0.007296
## inc_boroughQueens 0.007614
## inc_boroughStaten Island 0.012095
## al_source_descEMS 0.016444
## al_source_descEMS-911 0.016573
## al_source_descCLASS-3 0.008295
## al_source_descOthers 0.016989
## al_index_descInitial Alarm 0.010594
## al_index_descOthers 0.138817
## highest_al_levelFirst Alarm 0.132258
## highest_al_level2nd-3rd Alarm 0.272975
## inc_class_groupMedical MFAs 0.165233
## inc_class_groupNonMedical Emergencies 0.028832
## inc_class_groupNonMedical MFAs 0.041483
## inc_class_groupNonStructural Fires 0.094022
## inc_class_groupStructural Fires 0.063572
## engines_assigned 0.075363
## ladders_assigned 0.026255
## others_units_assigned 0.009331
## day_typeWeekend 0.013528
## time_of_dayMorning 0.009373
## time_of_dayAfternoon 0.009050
## time_of_dayEvening 0.009665
## tua_is_oneY 0.014267
## log(ladders_assigned + 1) 0.051175
## log(engines_assigned + 1) 0.122175
## log(others_units_assigned + 1) 0.021457
## inc_class_groupMedical MFAs:engines_assigned 0.925293
## inc_class_groupNonMedical Emergencies:engines_assigned 0.076905
## inc_class_groupNonMedical MFAs:engines_assigned 0.090673
## inc_class_groupNonStructural Fires:engines_assigned 0.110589
## inc_class_groupStructural Fires:engines_assigned 0.085034
## day_typeWeekend:time_of_dayMorning 0.017181
## day_typeWeekend:time_of_dayAfternoon 0.016467
## day_typeWeekend:time_of_dayEvening 0.017482
## inc_class_groupMedical MFAs:log(engines_assigned + 1) 1.421512
## inc_class_groupNonMedical Emergencies:log(engines_assigned + 1) 0.128675
## inc_class_groupNonMedical MFAs:log(engines_assigned + 1) 0.171467
## inc_class_groupNonStructural Fires:log(engines_assigned + 1) 0.266303
## inc_class_groupStructural Fires:log(engines_assigned + 1) 0.175949
## t value
## (Intercept) 13.138
## inc_boroughBrooklyn -26.073
## inc_boroughManhattan -5.746
## inc_boroughQueens -6.001
## inc_boroughStaten Island -10.155
## al_source_descEMS -1.681
## al_source_descEMS-911 -2.527
## al_source_descCLASS-3 4.011
## al_source_descOthers -29.404
## al_index_descInitial Alarm -2.877
## al_index_descOthers -0.536
## highest_al_levelFirst Alarm 0.704
## highest_al_level2nd-3rd Alarm -3.576
## inc_class_groupMedical MFAs 0.075
## inc_class_groupNonMedical Emergencies 14.803
## inc_class_groupNonMedical MFAs 13.857
## inc_class_groupNonStructural Fires -0.701
## inc_class_groupStructural Fires 6.839
## engines_assigned -2.610
## ladders_assigned 11.379
## others_units_assigned 0.594
## day_typeWeekend 0.269
## time_of_dayMorning -5.762
## time_of_dayAfternoon -8.985
## time_of_dayEvening -13.415
## tua_is_oneY -2.523
## log(ladders_assigned + 1) -13.559
## log(engines_assigned + 1) 3.432
## log(others_units_assigned + 1) -2.562
## inc_class_groupMedical MFAs:engines_assigned 1.917
## inc_class_groupNonMedical Emergencies:engines_assigned 4.453
## inc_class_groupNonMedical MFAs:engines_assigned 5.803
## inc_class_groupNonStructural Fires:engines_assigned 1.482
## inc_class_groupStructural Fires:engines_assigned 2.986
## day_typeWeekend:time_of_dayMorning -3.153
## day_typeWeekend:time_of_dayAfternoon -2.992
## day_typeWeekend:time_of_dayEvening 0.676
## inc_class_groupMedical MFAs:log(engines_assigned + 1) -1.827
## inc_class_groupNonMedical Emergencies:log(engines_assigned + 1) -7.887
## inc_class_groupNonMedical MFAs:log(engines_assigned + 1) -9.308
## inc_class_groupNonStructural Fires:log(engines_assigned + 1) -1.086
## inc_class_groupStructural Fires:log(engines_assigned + 1) -5.378
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## inc_boroughBrooklyn < 2e-16 ***
## inc_boroughManhattan 9.25e-09 ***
## inc_boroughQueens 1.99e-09 ***
## inc_boroughStaten Island < 2e-16 ***
## al_source_descEMS 0.092705 .
## al_source_descEMS-911 0.011513 *
## al_source_descCLASS-3 6.07e-05 ***
## al_source_descOthers < 2e-16 ***
## al_index_descInitial Alarm 0.004016 **
## al_index_descOthers 0.592004
## highest_al_levelFirst Alarm 0.481453
## highest_al_level2nd-3rd Alarm 0.000349 ***
## inc_class_groupMedical MFAs 0.940295
## inc_class_groupNonMedical Emergencies < 2e-16 ***
## inc_class_groupNonMedical MFAs < 2e-16 ***
## inc_class_groupNonStructural Fires 0.483595
## inc_class_groupStructural Fires 8.18e-12 ***
## engines_assigned 0.009070 **
## ladders_assigned < 2e-16 ***
## others_units_assigned 0.552494
## day_typeWeekend 0.787750
## time_of_dayMorning 8.44e-09 ***
## time_of_dayAfternoon < 2e-16 ***
## time_of_dayEvening < 2e-16 ***
## tua_is_oneY 0.011643 *
## log(ladders_assigned + 1) < 2e-16 ***
## log(engines_assigned + 1) 0.000601 ***
## log(others_units_assigned + 1) 0.010419 *
## inc_class_groupMedical MFAs:engines_assigned 0.055255 .
## inc_class_groupNonMedical Emergencies:engines_assigned 8.52e-06 ***
## inc_class_groupNonMedical MFAs:engines_assigned 6.61e-09 ***
## inc_class_groupNonStructural Fires:engines_assigned 0.138434
## inc_class_groupStructural Fires:engines_assigned 0.002830 **
## day_typeWeekend:time_of_dayMorning 0.001617 **
## day_typeWeekend:time_of_dayAfternoon 0.002771 **
## day_typeWeekend:time_of_dayEvening 0.498878
## inc_class_groupMedical MFAs:log(engines_assigned + 1) 0.067778 .
## inc_class_groupNonMedical Emergencies:log(engines_assigned + 1) 3.24e-15 ***
## inc_class_groupNonMedical MFAs:log(engines_assigned + 1) < 2e-16 ***
## inc_class_groupNonStructural Fires:log(engines_assigned + 1) 0.277667
## inc_class_groupStructural Fires:log(engines_assigned + 1) 7.59e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.366 on 22999 degrees of freedom
## Multiple R-squared: 0.1829, Adjusted R-squared: 0.1814
## F-statistic: 125.6 on 41 and 22999 DF, p-value: < 2.2e-16par(mfrow=c(2,2))
plot(lm_irm_full_upd_4)## Warning: non si riesce a fare il plot senza sfruttarne uno:
## 3682
residualPlots(lm_irm_full_upd_4)
## Test stat Pr(>|Test stat|)
## inc_borough
## al_source_desc
## al_index_desc
## highest_al_level
## inc_class_group
## engines_assigned -6.2667 3.753e-10 ***
## ladders_assigned -6.1606 7.368e-10 ***
## others_units_assigned -3.4382 0.0005866 ***
## day_type
## time_of_day
## tua_is_one
## log(ladders_assigned + 1) 8.1271 4.618e-16 ***
## log(engines_assigned + 1) 9.0977 < 2.2e-16 ***
## log(others_units_assigned + 1) 4.4294 9.494e-06 ***
## Tukey test 2.1411 0.0322669 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1qqPlot(residuals(lm_irm_full_upd_4))
## 11439 8399
## 11438 8399influenceIndexPlot(lm_irm_full_upd_4, vars = "Cook")
summary(fitted(lm_irm_full_upd_4))## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.6749 1.5995 1.7104 1.7008 1.8038 2.3965However we are still in a situation of non normal distribution of the residuals thus we can’t apply a linear regression model of the log scale of inc_resp_min_qy. Let’s see if in the other type response the assumption of linearity are meet or not (spoiler…they are not verified again :( ).
4.1.2 Use emergency_min_qy as response
Again we make a copy of the train and test. This time we decided to merge the assigned units in a single predictor deleting the single counts in order to see if we have an improvement on the qqPlots for the next models.
# make a copy of the train and test
emerg_min_fd.train <- fire_data.train
emerg_min_fd.test <- fire_data.test
emerg_min_fd.train$total_assigned_units = emerg_min_fd.train$engines_assigned + emerg_min_fd.train$ladders_assigned + emerg_min_fd.train$others_units_assigned
emerg_min_fd.test$total_assigned_units = emerg_min_fd.test$engines_assigned + emerg_min_fd.test$ladders_assigned + emerg_min_fd.test$others_units_assigned
# remove the future time differences and units counts
emerg_min_fd.train <- emerg_min_fd.train %>%
select(-c(inc_resp_min_qy, ticket_time, engines_assigned, ladders_assigned, others_units_assigned))
emerg_min_fd.test <- emerg_min_fd.test %>%
select(-c(inc_resp_min_qy, ticket_time, engines_assigned, ladders_assigned, others_units_assigned))Fit a linear regression model with all the predictors.
lm_em_full <- lm(emergency_min_qy ~ ., data = emerg_min_fd.train)
summary(lm_em_full)##
## Call:
## lm(formula = emergency_min_qy ~ ., data = emerg_min_fd.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -159.34 -8.44 -3.20 3.68 447.06
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 36.00960 5.65956 6.363 2.02e-10 ***
## inc_boroughBrooklyn -7.28090 0.29904 -24.348 < 2e-16 ***
## inc_boroughManhattan -1.01384 0.31406 -3.228 0.001247 **
## inc_boroughQueens -4.88731 0.32744 -14.926 < 2e-16 ***
## inc_boroughStaten Island -7.30118 0.52112 -14.011 < 2e-16 ***
## al_source_descEMS 1.65247 0.68751 2.404 0.016244 *
## al_source_descEMS-911 2.70914 0.69596 3.893 9.94e-05 ***
## al_source_descCLASS-3 -3.84839 0.34121 -11.279 < 2e-16 ***
## al_source_descOthers 3.70639 0.70369 5.267 1.40e-07 ***
## al_index_descInitial Alarm 16.42672 0.45649 35.985 < 2e-16 ***
## al_index_descOthers 96.50396 5.42673 17.783 < 2e-16 ***
## highest_al_levelFirst Alarm -31.00041 5.59102 -5.545 2.98e-08 ***
## highest_al_level2nd-3rd Alarm 230.75863 7.63898 30.208 < 2e-16 ***
## inc_class_groupMedical MFAs -0.77395 1.54247 -0.502 0.615842
## inc_class_groupNonMedical Emergencies -7.09947 0.66585 -10.662 < 2e-16 ***
## inc_class_groupNonMedical MFAs -2.00122 0.98708 -2.027 0.042632 *
## inc_class_groupNonStructural Fires 2.65601 1.03206 2.574 0.010073 *
## inc_class_groupStructural Fires -5.79816 0.85777 -6.760 1.42e-11 ***
## disp_resp_min_qy 0.13220 0.23913 0.553 0.580382
## inc_travel_min_qy 0.16048 0.04166 3.852 0.000117 ***
## day_typeWeekend -0.25255 0.23424 -1.078 0.280964
## time_of_dayMorning 1.33597 0.33836 3.948 7.89e-05 ***
## time_of_dayAfternoon 0.56196 0.32589 1.724 0.084647 .
## time_of_dayEvening -0.37739 0.34802 -1.084 0.278210
## tua_is_oneY -0.30932 0.39444 -0.784 0.432934
## total_assigned_units 1.38403 0.08355 16.565 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.78 on 23017 degrees of freedom
## Multiple R-squared: 0.3417, Adjusted R-squared: 0.3409
## F-statistic: 477.8 on 25 and 23017 DF, p-value: < 2.2e-16par(mfrow=c(2,2))
plot(lm_em_full)
Here the fitted values vs the residual are behaving in a liner relation but they are not randomly spread since we can view two / three clusters, the same thing discussion can be made for the Scale Location plot in which we can see that there is no constant variance. But again we are in a situation in which the residuals are not normally distributed as we can more clearly see in the following plot.
qqPlot(residuals(lm_em_full))
## [1] 17313 15855Let’s have a look of the possible power transformation of the response.
powerTransform(lm_em_full)## Estimated transformation parameter
## Y1
## 0.1454326We will try transform the response both using the logarithm scale and the power of 0.14. in order to see in we have an improvement on the distribution of the residuals.
First by using the suggested power trasformation of 0.14.
lm_em_full_014 <- update(lm_em_full, I(emergency_min_qy ^ 0.14) ~ .)
summary(lm_em_full_014)##
## Call:
## lm(formula = I(emergency_min_qy^0.14) ~ inc_borough + al_source_desc +
## al_index_desc + highest_al_level + inc_class_group + disp_resp_min_qy +
## inc_travel_min_qy + day_type + time_of_day + tua_is_one +
## total_assigned_units, data = emerg_min_fd.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.77825 -0.09195 -0.00581 0.09105 0.71297
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.2851931 0.0551223 23.315 < 2e-16
## inc_boroughBrooklyn -0.0776249 0.0029125 -26.652 < 2e-16
## inc_boroughManhattan -0.0089630 0.0030588 -2.930 0.003390
## inc_boroughQueens -0.0535928 0.0031891 -16.805 < 2e-16
## inc_boroughStaten Island -0.0888417 0.0050755 -17.504 < 2e-16
## al_source_descEMS 0.0135942 0.0066961 2.030 0.042352
## al_source_descEMS-911 0.0185578 0.0067784 2.738 0.006191
## al_source_descCLASS-3 -0.0524990 0.0033233 -15.797 < 2e-16
## al_source_descOthers 0.0138225 0.0068537 2.017 0.043728
## al_index_descInitial Alarm 0.2985189 0.0044461 67.142 < 2e-16
## al_index_descOthers 0.6474838 0.0528546 12.250 < 2e-16
## highest_al_levelFirst Alarm -0.0682250 0.0544547 -1.253 0.210263
## highest_al_level2nd-3rd Alarm 0.0687444 0.0744012 0.924 0.355512
## inc_class_groupMedical MFAs 0.0289789 0.0150232 1.929 0.053749
## inc_class_groupNonMedical Emergencies -0.0690382 0.0064852 -10.646 < 2e-16
## inc_class_groupNonMedical MFAs -0.0118967 0.0096138 -1.237 0.215931
## inc_class_groupNonStructural Fires -0.0088083 0.0100519 -0.876 0.380883
## inc_class_groupStructural Fires -0.0587682 0.0083544 -7.034 2.06e-12
## disp_resp_min_qy 0.0002734 0.0023291 0.117 0.906562
## inc_travel_min_qy -0.0006612 0.0004058 -1.630 0.103202
## day_typeWeekend -0.0021166 0.0022814 -0.928 0.353544
## time_of_dayMorning 0.0189708 0.0032955 5.757 8.70e-09
## time_of_dayAfternoon 0.0104510 0.0031740 3.293 0.000994
## time_of_dayEvening -0.0005981 0.0033896 -0.176 0.859931
## tua_is_oneY -0.0246653 0.0038417 -6.420 1.39e-10
## total_assigned_units 0.0096417 0.0008138 11.848 < 2e-16
##
## (Intercept) ***
## inc_boroughBrooklyn ***
## inc_boroughManhattan **
## inc_boroughQueens ***
## inc_boroughStaten Island ***
## al_source_descEMS *
## al_source_descEMS-911 **
## al_source_descCLASS-3 ***
## al_source_descOthers *
## al_index_descInitial Alarm ***
## al_index_descOthers ***
## highest_al_levelFirst Alarm
## highest_al_level2nd-3rd Alarm
## inc_class_groupMedical MFAs .
## inc_class_groupNonMedical Emergencies ***
## inc_class_groupNonMedical MFAs
## inc_class_groupNonStructural Fires
## inc_class_groupStructural Fires ***
## disp_resp_min_qy
## inc_travel_min_qy
## day_typeWeekend
## time_of_dayMorning ***
## time_of_dayAfternoon ***
## time_of_dayEvening
## tua_is_oneY ***
## total_assigned_units ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1537 on 23017 degrees of freedom
## Multiple R-squared: 0.2923, Adjusted R-squared: 0.2915
## F-statistic: 380.2 on 25 and 23017 DF, p-value: < 2.2e-16par(mfrow=c(2,2))
plot(lm_em_full_014)
qqPlot(residuals(lm_em_full_014))
## [1] 686 18514In this case the two tails appear to be more homogeneous, however the situation is the same so we do not have normal distribution of residuals as we can see by the qqPlot.
Trying the logarithm scale.
lm_em_full_log <- update(lm_em_full, log(emergency_min_qy) ~ .)
summary(lm_em_full_log)##
## Call:
## lm(formula = log(emergency_min_qy) ~ inc_borough + al_source_desc +
## al_index_desc + highest_al_level + inc_class_group + disp_resp_min_qy +
## inc_travel_min_qy + day_type + time_of_day + tua_is_one +
## total_assigned_units, data = emerg_min_fd.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.5221 -0.4348 0.0122 0.4897 3.3584
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.582598 0.286900 5.516 3.50e-08 ***
## inc_boroughBrooklyn -0.378681 0.015159 -24.981 < 2e-16 ***
## inc_boroughManhattan -0.043940 0.015920 -2.760 0.005786 **
## inc_boroughQueens -0.262438 0.016599 -15.811 < 2e-16 ***
## inc_boroughStaten Island -0.442181 0.026417 -16.738 < 2e-16 ***
## al_source_descEMS 0.057177 0.034852 1.641 0.100903
## al_source_descEMS-911 0.080740 0.035280 2.289 0.022116 *
## al_source_descCLASS-3 -0.266010 0.017297 -15.379 < 2e-16 ***
## al_source_descOthers 0.031943 0.035672 0.895 0.370547
## al_index_descInitial Alarm 1.662576 0.023141 71.846 < 2e-16 ***
## al_index_descOthers 3.093289 0.275097 11.244 < 2e-16 ***
## highest_al_levelFirst Alarm -0.278414 0.283425 -0.982 0.325952
## highest_al_level2nd-3rd Alarm -0.138134 0.387242 -0.357 0.721310
## inc_class_groupMedical MFAs 0.240270 0.078192 3.073 0.002123 **
## inc_class_groupNonMedical Emergencies -0.338830 0.033754 -10.038 < 2e-16 ***
## inc_class_groupNonMedical MFAs -0.018906 0.050038 -0.378 0.705551
## inc_class_groupNonStructural Fires -0.076189 0.052318 -1.456 0.145330
## inc_class_groupStructural Fires -0.298421 0.043483 -6.863 6.92e-12 ***
## disp_resp_min_qy 0.001249 0.012122 0.103 0.917958
## inc_travel_min_qy -0.007062 0.002112 -3.344 0.000827 ***
## day_typeWeekend -0.009696 0.011874 -0.817 0.414182
## time_of_dayMorning 0.092398 0.017153 5.387 7.24e-08 ***
## time_of_dayAfternoon 0.051043 0.016520 3.090 0.002006 **
## time_of_dayEvening -0.001901 0.017642 -0.108 0.914173
## tua_is_oneY -0.132984 0.019995 -6.651 2.98e-11 ***
## total_assigned_units 0.046169 0.004235 10.901 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7998 on 23017 degrees of freedom
## Multiple R-squared: 0.2978, Adjusted R-squared: 0.2971
## F-statistic: 390.5 on 25 and 23017 DF, p-value: < 2.2e-16par(mfrow=c(2,2))
plot(lm_em_full_log)
Again we note the presence of three clusters on the first and third plots, let’s investigate a bit in order to gain some additional information.
ggplot(lm_em_full_log, aes(x = .fitted, y = .resid)) +
geom_point(aes(color = inc_class_group)) +
geom_hline(yintercept = 0) +
labs(title = "Residuals VS Fitted",
x = "Fitted Values", y = "Residuals", color = "Incident Class Group")
The right cluster is for the Structural Fires, the middle one contain both Medical and NonMedical Emergencies with some Strictural and NonStructural Fires, and the left one contains NonMedical Emergencies and a small number of Medical one and Medical and NonMedical MFAs.
qqPlot(residuals(lm_em_full_log))
## [1] 686 18514Here the right tail is less far from the 95 confidence interval respect the previous model, but on the other hand the left tail is heavily skewed to the bottom of the interval. Indicating that again we do not reach the normal distribution of the residual.
In conclusion we end up in a situation where the linearity assumptions are not meet thus we can’t use a regression model to perform prediction even with the logarithm transformation of the response. It is much likely that a powerful methods should be taken into account for this analysis with a deeper study of the relationship between predictors.
4.2 Cast the anaysis to a Calssification task
As mention before we decided like the professor suggested to us, to cast our regression problem in a classification problem by dividing the range of possible time difference response into 2 for a binary classification or more than 2 for a multi-classification task.
We will use the same predictors of the Regression Section so first inc_resp_min_qy and then emergency_min_qy.
So first thing first we have to decide the range of value for both of them.
summary(fire_data_new$inc_resp_min_qy)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.350 4.383 5.467 5.949 6.850 58.917summary(fire_data_new$emergency_min_qy)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.05 7.15 11.93 17.08 19.58 596.38We start by considering a classical binary classification in which the threshold used as response is the mean of the respective responses, thus:
# threshold for inc_resp_min_qy
th_irm <- summary(fire_data_new$inc_resp_min_qy)[4]
# threshold for emergency_min_qy
th_eme <- summary(fire_data_new$emergency_min_qy)[4]4.2.1 Use the range of inc_resp_min_qy as response
# make a copy of the train and test
cl_resp_min_fd.train <- fire_data.train
cl_resp_min_fd.test <- fire_data.test
cl_resp_min_fd.train$fast_response <- cl_resp_min_fd.train$inc_resp_min_qy < th_irm
cl_resp_min_fd.test$fast_response <- cl_resp_min_fd.test$inc_resp_min_qy < th_irm
# remove the future time differences
cl_resp_min_fd.train <- cl_resp_min_fd.train %>% select(-c(disp_resp_min_qy, inc_travel_min_qy, emergency_min_qy, ticket_time, inc_resp_min_qy))
cl_resp_min_fd.test <- cl_resp_min_fd.test %>% select(-c(disp_resp_min_qy, inc_travel_min_qy, emergency_min_qy, ticket_time, inc_resp_min_qy))glm.fit_full <- glm(fast_response ~ ., data = cl_resp_min_fd.train, family = binomial)
summary(glm.fit_full)##
## Call:
## glm(formula = fast_response ~ ., family = binomial, data = cl_resp_min_fd.train)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.59233 1.20858 0.490 0.624059
## inc_boroughBrooklyn 1.08113 0.04189 25.808 < 2e-16 ***
## inc_boroughManhattan 0.19367 0.04249 4.558 5.15e-06 ***
## inc_boroughQueens 0.34738 0.04421 7.857 3.92e-15 ***
## inc_boroughStaten Island 0.77875 0.07233 10.767 < 2e-16 ***
## al_source_descEMS 0.37809 0.09838 3.843 0.000121 ***
## al_source_descEMS-911 0.38790 0.09944 3.901 9.58e-05 ***
## al_source_descCLASS-3 -0.24070 0.05044 -4.772 1.83e-06 ***
## al_source_descOthers 0.68813 0.11228 6.129 8.87e-10 ***
## al_index_descInitial Alarm 0.14764 0.06012 2.456 0.014065 *
## al_index_descOthers -1.84737 1.12910 -1.636 0.101810
## highest_al_levelFirst Alarm -1.21307 1.20160 -1.010 0.312711
## highest_al_level2nd-3rd Alarm 4.12543 71.67297 0.058 0.954100
## inc_class_groupMedical MFAs -0.14191 0.20432 -0.695 0.487338
## inc_class_groupNonMedical Emergencies -0.14312 0.09537 -1.501 0.133434
## inc_class_groupNonMedical MFAs 0.10486 0.13903 0.754 0.450713
## inc_class_groupNonStructural Fires 0.53125 0.15826 3.357 0.000788 ***
## inc_class_groupStructural Fires 0.28383 0.12945 2.193 0.028336 *
## engines_assigned 0.32005 0.02633 12.154 < 2e-16 ***
## ladders_assigned -0.03555 0.04025 -0.883 0.377146
## others_units_assigned 0.22656 0.03493 6.485 8.86e-11 ***
## day_typeWeekend 0.14590 0.03272 4.458 8.26e-06 ***
## time_of_dayMorning 0.38885 0.04611 8.433 < 2e-16 ***
## time_of_dayAfternoon 0.54527 0.04462 12.222 < 2e-16 ***
## time_of_dayEvening 0.79213 0.04833 16.389 < 2e-16 ***
## tua_is_oneY -0.90479 0.05733 -15.783 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 30976 on 23042 degrees of freedom
## Residual deviance: 27741 on 23017 degrees of freedom
## AIC: 27793
##
## Number of Fisher Scoring iterations: 10glm.probs <- predict(glm.fit_full, newdata = cl_resp_min_fd.test, type = "response")preds50 <- glm.probs > 0.5
table(preds = preds50, true = cl_resp_min_fd.test$fast_response)## true
## preds FALSE TRUE
## FALSE 1340 803
## TRUE 1711 3828mean(preds50 == cl_resp_min_fd.test$fast_response)## [1] 0.6727415The ROC curve can be computed with package pROC:
library(pROC)
glm.roc <- roc(cl_resp_min_fd.test$fast_response ~ glm.probs, plot = TRUE, print.auc = TRUE)